Instructions
Change Windows Live ID
Turn on the Xbox 360 that has the gamertag on it. Wait for the dashboard to load.
Press the Xbox 360 logo on your controller. This will bring up the Xbox 360 guide screen.
Press right on your controller to go to the "Settings" tab. Select "Account Management."
Select "Windows Live ID" and then choose "Change Windows Live ID."
Select "Yes I do." Enter the new Windows Live ID you would like to set as the one for your account.
Recover Gamertag
Turn on the Xbox 360 for which you would like to recover the Xbox 360 gamertag.
Press the Xbox 360 logo button on the center of your controller.
Select "Recover Gamertag" from the list of options on the Xbox Guide.
Press "A" to go to the next screen. Enter the new Windows Live ID that you have just set for your account and then enter the password for that ID.
Wait for the download process to be completed and you will have now successfully recovered your gamertag.