Initial Mac Setup to work with WiFi Router / Airport Base Station
This is a quick, terse walkthrough of screenshots taken
under OS X 10.3.7 to set up a Powerbook to use a Wireless Router that is already running (with another computer.)
The same procedure should work with almost any WiFi Router (e.g. LinkSys, NetGear, DLink, SMC, Asante...),
though I have another page dedicated to completely seting up a LinkSys here.)
(A similar page with OS X 10.2 screenshots is here.)
Pertinent AppleCare KnowledgeBase articles
Initial Mac Setup to work with Airport Base Station
In order to use the Mac to access the internet through the Airport Base Station:
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Open Network Preferences from OS X's System Preferences.
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Set up a New Location for this configuraton. (This is instead of changing your current configuration, so you can go back to it easily if something gets munged.)
Pick New Location from the pull-down menu next to "Location:" on Network Preferences.

(this screenshot has a few extra locations from my system.
You'll probably have only one existing Location, "Automatic".)
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In the dialog that appears, Enter a name, such as "Airport", for this Location.
Any name you like will do. It will show up in the Location menu later.

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Switch the "Location" pull-down to the new "Airport" Location (or whatever you named it.)
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Set the "Show:" pull-down menu to Network Port Configurations in the Network Preference dialog.

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Make sure the Airport and Built-In Ethernet are both checked (that means they are enabled;
if you don't have an Airport card installed, the option won't show up.
If you never want to use one o fthe interfaces shown, you can uncheck it).
If you want to still use dial-up, you can check Internal Modem, too.
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You can click and drag on an item on the list to move it up and down the list.
The order in which these appear in the list is the order in which the Mac tries to use the interfaces.
You can put either Built-In Ethernet or Airport on top (I suggest Airport if you're using one) but you probably want both above the Internal Modem.

This determines the order in which your Mac will use the connection.
If you list Airport first, then the Mac will use it as long as the Airport is on and has a signal.
If you have Ethernet first, then the Mac will use it as long as it has a connection (the catch being, depending on your network settings, the Mac can't always tell if the Ethernet runs to a working internet connection.)
If you have Dial-up on top, the Mac will try to dial the modem rather than use a perfectly good airport or Ethernet connection.
I keep my Airport at the top of the list and manually turn airport Off from the menubar status menu when I dock to the Ethernet cable.
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Set the "Show:" pull-down to Airport.

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Select the TCP/IP tab.
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Set the "Configure:" pull-down menu to "Using DHCP".

Using DHCP here means your Mac will obtain its IP address, netmask and router address automatically from
the LAN DHCP server in the WiFi Router.
Once the Mac connects to the Base Station, this screen will show (in grayed text) the actual assigned IP Address,
Netmask, and Router address obtained from the router.
With the Airport Base Station (default setup), the IP Address will be at the lower end of the range 10.0.1.2 - 10.0.1.100,
the netmask will be 255.255.255.0 and the router will be 10.0.1.1. Airport Extreme Base Stations and ther brands will assign addresses in the range 192.168.0.1 - 192.168.2.255, depending on brand.
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Select the Airport tab.
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Set the Option to remember your password on the Keychain if you want.
Set the "allow computer to create networks" if you want.
(This is for ad hoc Mac-to-Mac wireless networks without a base station or router.)
Set "Show Airport Status in menu bar" if you like.
(This is convenient for checking status and opening Internet Connect.)

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Click Apply Now. That should do it.
(You don't need any AppleTalk or Proxy settings.)
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Open the Internet Connect application (Applications/Utilities folder), or from the Airport icon in menu bar.
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Make sure the "Airport Power:" says On. (This is the status or your Mac's Airport card.)
If not, click "Turn Airport On" button.

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Make sure the Network: pull-down shows the name of the WiFi Router
(the SSID name on the Airport Base Station is preset, but can be changed with the Airport Admin Utility, e.g. "Airport". Mine is named "BCblue").
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You should show a signal.
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If the network is protected by a WEP password, you will be prompted to enter the password.
- If you are using an Apple Airport Base Station, leave the Wireless Security pulldown set to "WEP Password" and enter the Pass Phrase you used when you set up the Airport Base Station with the Airport Admin Utility.

- If you are using a non-Apple WiFi Router, set the Wireless Security pulldown set to "WEP 40/128-bit Hex":

Look up the hexadecimal key for your WiFi network on your WiFi router.
A "128-bit" WEP key will be 26 digits long (each hexadecimal digit is between 0-9 or A-F; and you need to get every one of them right!).
How you get this from your router depends on the brand of your Router.
Check it's configuration utility, Wireless / Security screen, e.g..
Here's where the LinkSys configuration utility shows it:

Enter those 26 digits in the "WEP password" field:

Your Mac is now set up so it can connect to the Internet either wirelessly or wired.
Once you are successfully connected to the router, you can verify a good connection by checking
the System Preferences's Network preference Pane, TCP/IP tab.
A good connection should show that an IP Address has been assigned by the base station's DHCP server.
For an Airport base station, this will be an IP address in the range 10.0.1.2 - 10.0.1.199.

Other brands of routers can assign IP adderesses starting with "192.168.".
An IP Address starting with "169." is not valid IP address on the LAN - it's self-assigned, and means there is a problem.
Now open Safari and go surfing.
If you havenet already configured your WiFi Router, and it's not an Apple Airport Base Station,
use the browser to view the Router's setup pages. E.g.
URL http://192.168.1.1 or http://192.168.0.1,
or whatever your Router's manual says, by typing that address in the URL address bar.

Specific instructions for seting up a LinkSys here
You can check the rest of my home network config info here.
If something above seems missing, confusing or down-right wrong, you can eMail me as car1son at my .Mac account.
(Please be specific at what point things went wrong and how they went wrong.)
Good luck!