Much of the history of Old English writing is unknown in its details because the Anglo-Saxon settlers were not literate. The earliest written records of Old English date from around 700 A.D.
Early Germanic tribes had a runic alphabet, but it was only used for mystical, magical, or secret religious purposes, not as a tool for communication. The first writing in Old English was done after the Christianizing of England by monks using the Roman alphabet of their Latin to approximate the sounds of Old English they heard from the populace around them.
The early writing thus lacked the graphemes (letters) "j", "k", "q", and "v". In addition, because the Roman alphabet had no letters to correspond with certain Old English sounds, additional letters were added: "æ", "þ", "ð", "", and "". The "þ" and "" come from the runic alphabet; the "æ" is simply a ligature of the letters "a" and "e" (though the name of the letter, the "aesc" or "ash", comes from its runic name); the history of the "" is conjectural; and the "ð" is an adaptation of the letter "d" used by Irish monks.
Abbreviation was a common scribal practice, as copying manuscripts was an extremely tedious process at best. Vowels could be omitted from common words (þt =þæt). Perhaps the most common scribal convention was the "nasalized macron," used to indicate a nasal consonant after a vowel in common words (þã means þan "than").
Click here to see a complete chart of the entire OE alphabet.