Xbox Live works both in wired and wireless configurations, but as you can expect, set-up for the latter is more complicated. Because additional equipment is involved, you'll need to follow several steps beyond those for a wired connection and have on hand some information about your wireless connection.
Make sure you have a properly working high-speed Internet connection and that the connection from the wall to the modem and ultimately to the wireless router is fully functioning--the connection should have regular browsing and downloading capabilities.
Look in your wireless router's documentation and find the web address for its set-up console. Find and write down the SSID and WEP numbers for your wireless router. Also, make sure you know the name of the wireless network you use with your PC and any passwords associated with it.
Plug the Xbox 360 wireless networking adaptor into the back of the console--use the USB port. Look for the light indicator on the adaptor. The light should appear either solid green or solid red. Solid green means the adaptor is good to go, and most likely a connection to Xbox Live will launch with no additional set-up. Solid red means you need to configure your set-up. Proceed to the next step.
Go to "My Xbox" on the Xbox dashboard and select "System Settings" followed by "Network Settings." Choose "Configure Network" and make sure the SSID and WEP numbers that appear there match the ones you recorded off the router set-up on your PC. If they do not match, enter the correct numbers manually.
Go to the "Basic Settings" tab and select "Wireless Mode." This brings up a list of any wireless networks detected by the adaptor. Select the one used by your PC if available, entering any passwords as needed.
Select "Apply," followed by "Test." This causes the console to go through a Live connectivity test akin to the one used in wired connections. Once an IP address appears, the console should able to connect to the Internet.
If the Xbox Live test fails, turn the console off and restart it after at least 30 seconds. Check the adaptor light--if it's a solid red, go over the set-up steps again. Problems typically occur in router set-up, namely the console's inability to match router settings. This stems from routers being inherently difficult to moderate in relation to other devices. Whenever possible and convenient, choose a wired connection--the more direct, the better. If you can get by with connecting a broadband wire from the wall to the Xbox console, all the better. Not only does this cut out set-up hassle, it also guarantees a faster, less latent connection.