Instructions
Load your Xbox 360 to the dashboard. Sign in to the account with which you intend to join Xbox LIVE.
Press "A" on your avatar under the "My Xbox" category. Pick "Join Xbox LIVE" from the list that appears.
Type in the requested information. This includes the email and password associated with your account, your full name, address and date of birth. You will also have the option to attach a credit card to your account if you wish to upgrade to an Xbox LIVE Gold membership, but this is not mandatory. When you complete this process, the console will assign you a gamertag and return you to the dashboard.
Press "A" on your avatar again. This time, pick "Change Gamertag" from the list.
Press "A" on either "Enter New Gamertag" to type in your own custom name or "Get Suggestions" to have the console make suggestions for you. Select one of the provided names or type in your own and press "Start."
Press "A" on "Yes, use this gamertag" when you are satisfied with your choice.