Instructions
Turn on your Xbox 360 and make sure there are no games in the tray.
Select "My Xbox" on the Xbox Dashboard. Then, select your avatar.
Choose the "Join Xbox Live" option.
Input your email address and other relevant information when prompted. You will also have to accept Microsoft's terms of use. If you purchase a "Gold" membership, you will have to enter your credit card information as well; this is not necessary if you sign up for a free membership.