First things first.  If you want to know about the Green Lanterns, you first have to know about the who they were created by... 

The Guardians of the Universe:

The Guardians evolved on the planet Maltus, and were possibly the first intelligent life forms in the Universe. At this time they were tall greyish blue humanoids with black hair. They became scientists and thinkers, experimenting on the worlds around them. One experiment led to the creation of a new species, the Psions. In a pivotal moment, billions of years ago, a Maltusian named Krona used time-bending technology to observe the beginning of the Universe. This experiment flooded the beginning of the Universe with entropy causing it "to be born old". (This is a retcon; originally, the experiment created evil, and splintered the Universe into the Multiverse).

Feeling responsible for this, the evolved Maltusians relocated to the planet Oa (at "the center of the Universe") and became the Guardians. Their goal was simple: combat evil and create an orderly universe. And they acted quickly on that goal. During this period they also changed to their current appearance. They serve as the administrators of the Green Lantern Corps, an interstellar police force which patrols the universe.

When Rayner briefly becomes the godlike Ion, he possesses more power than Hal Jordan did as Parallax. Realizing that he can not continue as Ion without losing his humanity, Kyle travels to the recently restored Oa to recharge the Central Battery. By doing so, he creates a new set of Guardians, this time as small children (both male and female), with the intent that Ganthet will look after them and teach them how to be better Guardians than their predecessors.

Following the return of Hal Jordan, all the Guardians have aged to adulthood and are just as cold and manipulative as before. Ganthet, of course still retains a sense of individuality amongst the Guardians, believing that they should retain their emotions.

Ganthet:

Ganthet is one of the Guardians of the Universe. However, where most of the Guardians are very stern 'by-the-book' characters, Ganthet has a personality that is more human-like, including displays of empathy and concern for an individual, instead of only thinking of the Green Lantern Corps. In various DC crossover limited series, Ganthet is shown as being part of the Quintessence, a group of near-omnipotent beings who oversee the results of what happens on Earth.

Hal Jordan:

When the dying Abin Sur crash-landed on Earth and ordered his power ring to seek out a suitable successor as Green Lantern of space sector 2814, test pilot Hal Jordan met the requirements of being both honest and without fear. Hal was one of the first of a new age of costumed adventurers, defending his home town of Coast City as well as the world from villains and menaces both earthbound and alien. Hal united with the Flash, Aquaman, Martian Manhunter, and Black Canary to form the Justice League of America. As a ring wielder, Hal was a member of the 3,600-strong Green Lantern Corps and was trained in part by Sinestro, who would become a renegade and one of his greatest foes. The Corps were the universe's most revered peacekeepers, and it was not long before his bravery earned Hal the respect of both his peers and the Guardians of the Universe, who created the Corps. He heroically championed the Guardians' goal to preserve order throughout the galaxies, even when their orders ran contrary to Hal's own rigid sense of morality. Yet, Hal was not above confronting the Guardians or quitting the Corps in order to pursue his own ideals, but he always returned to the fold.

Hal was perhaps the Oans' and the Corps' greatest champion.

Ironically, Hal would also be their undoing. When Coast City was decimated by Mongul and the Cyborg Superman, Hal was denied the power to resurrect the city and its inhabitants by the Guardians. He set out for Oa to gain the power to set things right. The Guardians set the Corps against him, including the reconstituted Sinestro, whom he killed. Hal entered the Central Power Battery and absorbed its emerald energies, and then renamed himself Parallax. Hal then attempted to amend the great wrong by changing the time-space continuum, but was thwarted by Earth's heroes, including new Green Lantern Kyle Rayner, who would clash with Parallax several times. In the end, however, Hal proved he had not strayed from the path of the hero. During Earth's final night, Hal used all his energies to reignite Earth's sun, redeeming himself in death.

While dead, Hal took up the mantle of the Spectre (the Spirit of Vengeance and quite possibly the most powerful character in all of comics) to atone for his sins while he was Parallax.  During the "Green Lantern: Rebirth" series, it was discovered that Parallax was actually an entity that bonded itself to Jordan's soul and was responsible for all that damage that was done. Jordan was eventually freed of this creature and is now helping to rebuild the GL Corps as well as clear his name in many people's eyes.

Kyle Rayner:

To put in bluntly, Kyle was in the right place at the wrong time.  Or depending on his state of mind or who was pounding him into the pavement that day, the wrong place at the wrong time.

After Hal Jordan became Parallax, Ganthet, the last surviving Guardian of Oa, was entrusted with finding a new and last Green Lantern.  He constructed a new ring, one which did not have the weakness against anything yellow and could also hold a charge much longer than 24 hours (as all previous rings had those limitations).  Ganthet arrived on Earth and gave the ring to Kyle telling him to "do what he must".  Kyle put on the ring and his life was never the same.

After being confused with Hal, one of the first things Kyle did as GL was radically change his costume to reflect the changing of the guard.  He soon joined the Titans but was traded up to the big league, the JLA, when it reformed with the "Big 7" (Superman, Wonder Woman, Batman, Flash, Martian Manhunter, Aquaman, and Green Lantern). 

Although Kyle was not trained as a typical Green Lantern would have been, he's managed to keep himself relatively out of trouble.  His insecurities, however, do threaten to overwhelm him at times.  Kyle wants to live up to the name of Green Lantern, but he knows what happened to Hal and understands that it could easily happen to him if he slips up.  The Oan Power ring is the most powerful weapon in the universe. He's considered giving it up but knows that's not what he's about.  It's his ring.  Literally.  The ring is bonded to his DNA and no one else (besides a close blood relative) can use the ring.  During his time as Ion, he made other changes to the ring.  One being that it can't be taken away from him or it comes right back, and the other was to give the ring a "reserve tank" of energy so that it would never run out of power when he needs it most.

For a brief period, Kyle achieved godhood as Ion. This was after he absorbed the energy Hal Jordan had left in Earth's sun during the Final Night incident, energy which had merged and grown with energies released after Oblivion's defeat. With his new powers, Kyle could bend time, space, and reality. This turned out to be too much for him and he willingly gave up all the power to reignite the Central Oan Power Battery so that the GL Corps could be restarted.

With Hal's resurrection, Kyle no longer operates on Earth. He was given his first official Green Lantern Corps assignment from Kilowog, and met with the Guardians, along with Guy Gardner, about his role in the Corps. There, he is given special status amongst the Guardians, who consider him the "Torch-Bearer," the Green Lantern who carried the legacy through the Corps' darkest period.
Most recently, Kyle has been a pivotal player in the Sinestro Corps War. The entitly known as Parallax was joined with Kyle to battle against Hal and the rest of the Corps.

Kyle does survive this trial and dons yet another GL costume - a combination of the traditional GL uniform and the one that he wore during most of his carreer (the one that GL-ND is based off of). Kyle will once again need a ring, and he'll be wearing his old "crab-mask". While no longer possessing the entity known as "Ion", Kyle has rejoined the Corps and has been partered with Guy Gardner.

Jade:

Jenny-Lynn Hayden's normal adolescence came to an abrupt end when the green birthmark on her left palm began to pulse, providing her with access to a strange green energy similar to the type used by Earth's Green Lanterns. The pulse's power permanently altered her body, making her hair and skin green. As with a Green Lantern, her willpower controls this energy, which she learned to channel through a variety of means. Unlike a Green Lantern, Jenny-Lynn - who adopted the code name Jade - needs no power ring to focus her powers or battery to recharge it.

Eventually Jenny-Lynn and her brother Todd (who had shadow-based powers and called himself Obsidian) learned that Green Lantern Alan Scott was their biological father, and their mother was Rose Forrest, the super-villain known as Thorn. Their father's prolonged exposure to his ring's energy, having altered his chromosome structure, was the likely cause of the siblings' mutations.

A member of Infinity, Inc. until it disbanded, Jade gave up super-heroics when she lost her powers and turned her attention to modeling and acting, but found her true passion as a photographer. Jenny-Lynn met and fell in love with Kyle Rayner.

For a time, she used a GL ring (given to her by Kyle as an engagement ring) to help fight the good fight.  But, thanks to genetic manipulation courtesy of Kyle (during his time as the nigh-omnipotent Ion), Jenny once again wields emerald energies. Though she has, on occasion worn a Green Lantern uniform, she prefers to be known as "Jade," a sobriquet she first used as a founding member of Infinity Inc.

Recently, Kyle and Jenny broke up and have gone their separate ways.  Jenny joined the Outsiders for a breif time. In the Rann-Thanagar War Infinite Crisis Special, Jen dies trying to stop Alexander Luthor, Jr. from tearing the universe into a Multiverse. Her consciousness lingers in her power, at least until her inherited Starheart powers merged with Kyle. This transfer instigates Kyle's second metamorphosis into Ion.

Guy Gardner:

When Green Lantern Abin Sur had to choose between Guy Gardner and Hal Jordan to succeed him, Jordan was closer and Guy seemed a mere footnote in history. Inevitably Guy became a member of the GL Corps, joined the Justice League and once proclaimed himself the one, true Green Lantern.

Though known as a hot-headed brawler, few questioned Guy's heroism, even when he wore the yellow ring of rogue GL Sinestro. When it was destroyed, it appeared Guy's super-heroing days were again over.

Yet, within him were genes of the extinct Vuldarian race, which granted him incredible powers once they manifested, including the ability to transform any part of his body into a weapon.

During Green Lantern: Rebirth, Gardner's Vuldarian DNA is strangely overwritten by his human DNA when Parallax possesses Gardner and several Green Lanterns. Hal Jordan's ring splits in two and Gardner's ring is restored to him. Eventually, Parallax is defeated by the combined effort of all five active Green Lanterns, including Gardner. The Guardians then select Gardner as one of the senior officers of the new Green Lantern Corps.

Alan Scott:

While working as an engineer, Scott discovered a mystical lantern that had been carved from an ancient meteor known as the Starheart. Manufacturing a ring from the same lantern, Scott was able to tap into the Starheart's occult energies, allowing him to assume the guise of the costumed mystery man, Green Lantern.

In the wake of the Zero Hour crisis, Scott's power ring was destroyed by Extant, which seemingly ended Scott's career as Green Lantern . Since then, Scott has learned that his prolonged exposure to the Starheart's energy has permanently imbued his body with its "green flame." Scott continues his crusade against the forces of darkness, fighting alongside the newly revitalized JSA.  Alan was also the first person to give Kyle his first history lesson about the GL Corps and how he came to have his ring in the first place.

John Stewart:

Hand-picked by Hal Jordan to be his successor, John Stewart butted heads with his superiors, but served heroically as a member of the Green Lantern Corps. He married a fellow GL, Katma Tui, and the two moved to Earth when the Corps disbanded. However, their happiness was short-lived when Katma was killed by Star Sapphire.

His greatest failure came when his overconfidence in his power ring allowed the planet Xanshi to be destroyed. To make amends, John spent time as the protector of Mosiac, a patchwork world created by a mad guardian. Leaving Mosiac, he joined the Darkstars only to be crippled by Grayven while defending the planet Rann. He found solace as an architect and thanks to Hal Jordan, has regained the use of his legs.

When Kyle left Earth for personal reasons and made John his replacement in the JLA. Currently, John is working with the GL Corps on Oa.

Major Force:

When Kyle first started his career as Green Lantern, one of the first individuals he encountered was Major Force.  On a mission to "retrieve" the ring from Kyle, he killed his girlfriend Alexandra and placed her body in Kyle's refrigerator to find.  This had the opposite effect on Kyle as he almost killed Major Force if Guy Gardner wasn't there to stop him.

Major Force was created when Sgt. Clifford Zmeck was offered the choice between a life sentence for murder or becoming a test subject where he was subjected to the same experiment that created Captain Atom. Zmeck received a double coating of the alien alloy in addition to super-strength, flight, invulnerability, and the ability to project energy blasts. He is also immortal, as he has died many times, only to return. A loyal soldier, Major Force does whatever dirty work his country demands, which has brought him into conflict with Captain Atom among other heroes. His vilest deed was murdering Green Lantern Kyle Rayner's girlfriend, an act which was eventually repaid when Major Force's decapitated head was jettisoned into space.

Major Force reappeared in the new Battle for Blüdhaven book, a title set a year after the events of Infinite Crisis, as the field leader of project S.H.A.D.E. In issue #5, he ripped the right arm off a government hero named Major Victory, and beat him to death with it. However, Captain Atom was revived by the Atomic Knights in issue #6, and Force's rampage was quickly brought to an end when Atom drained him of his energy, leaving nothing but a husk. Force's corpse was last seen falling into the chaos left by the destruction of Blüdhaven at Atom's hand.

Now that you're a little bit more familiar with the GL characters, you may not really understand what a GL ring (otherwise known as an Oan Power Ring) can do.

Power rings typically hold a limited charge. Originally, they required recharging every 24 hours, but more recently it seems that they possess a fixed amount of regular charge. Power rings are usually recharged by a Green Lantern's personal power battery, which looks like an old fashioned lantern made of dark green metal. The user typically points the ring towards the lantern, and usually gives a Green Lantern oath (below) while recharging the ring. These batteries are directly linked to the Central Power Battery on Oa and do not themselves need recharging.

Green Lantern Corps rings typically reserve a small portion of their power for a passive force field that "protects the wielder from mortal harm". In dire emergencies, that energy reserve can be tapped, at the expense of said protection, until it too is exhausted.

For a very long time, power rings were unable to affect objects colored yellow. Lanterns have typically found ways to get around these limitations by affecting objects indirectly. For example, if the Lantern is faced with a yellow gas approaching him, a fan can be created to blow it away since the fan only directly affects the normal air around it, not the gas. Originally, it was believed that the "yellow impurity" was implanted deliberately because the Guardians wanted the rings to have a weakness to prevent a Green Lantern from becoming all-powerful. More recent events have revealed that the "yellow impurity" was in fact caused by a yellow energy being, named Parallax, made of pure fear imprisoned in the Central Power Battery. Following the defeat of this creature during "Green Lantern: Rebirth", an experienced wielder of a power ring can, with effort, overcome the yellow weakness by recognizing the fear behind it, and facing that fear.

By far, the most significant limitation of the power ring is the willpower of the wielder. Mind control, hallucinogens, psychic attacks, "neural chaff" and other phenomena that disrupt thought processes will all indirectly impair a power ring's effectiveness. More abstractly, so can a weakening of resolve and will. For example, during the Millennium crossover, Hal Jordan fights a Manhunter who psychologically attacks him, to make him doubt that the people he is protecting value the principles he is fighting for. Jordan's resolve begins to weaken and his ring loses effectiveness until one of his charges strikes the Manhunter, declaring that she does deeply value Jordan's principles as well. With this dramatic affirmation, Jordan's faith in his cause is restored and the ring instantly returns to full power. The ring, though, does have some psychic defenses: Guy Gardner's ring apparently is able to put up psi-shields around him and Blue Beetle in their battle against the Ultra-Humanite.

The ring is programmed to prevent the wielder from killing sentient beings. Any attempt will be diverted by the ring, and in some cases may result in the ring locking out the user.

In "Green Lantern: Rebirth" it is revealed that only a certain type of willpower can use the ring effectively, or rather, that the willpower must be pure. Examples are Green Arrow's attempt to use Hal's ring leave him exhausted due to his will being marred by cynicism.

The GL Corps originally consisted of the 3600 members from across the universe.  Each sector of space was assigned it's own GL for protection and policing.   When the Corps was brought back, each sector was assigned two GL's (much like police officer's have partners) so now the total is 7200. Earth is sector 2814.

The Green Lantern Oath was used long before Kyle came around, so for a long time he did not use it.  However, he has picked it along the way.  It was said each and every time the ring was charged against the GL's battery.  Kind of like the Pledge of Allegiance, it reminds the GL of his/her duty.  The oath is:

"In brightest day, in blackest night,
no evil shall escape my sight!

Let those who worship evil's might,
beware my power... Green Lantern's light!"

A Power Battery is given to each GL so that their ring can be recharged when needed.  It's also considered one of the strongest sources of raw power in the universe.  Each battery is a piece of the Oan Central Power Battery and can tap into it's vast energy sources.  Without it, the GL ring is useless.