Follow these steps if you are trying to use a laptop :
Make sure that your XBOX 360 is fully functional and your laptop is connected to the internet by means of a wireless card.
Locate the Ethernet cord and connect it to both the computer and XBOX 360. Don't turn on the XBOX 360 yet.
On your Vista, click "Start" then "Network". After select the tab "Network and Sharing Center." On the left tab, click on "Manage network connections." You will see a Local Area Connection and a Wireless Internet Connection.
Use your mouse to select both icons and right click. Click on Bridge Connections. Turn on your XBOX 360, Sign In, and you will find yourself connected to XBOX LIVE.
Once you are done, and you need to use your computer for other uses. Simply right click on the Bridge Connection and select disable.
For more information on how to connect and use xbox go to the link below you will find all the details :