Instructions
Power on the Xbox 360 that you want to transfer your gamertag to.
Log off of any profiles if they signed in automatically upon start-up.
Press the "Guide" menu button on your controller (the button with the Xbox symbol on it). The Guide menu pops up on the screen.
Select "Recover Gamertag" from the Guide menu list. Another window will appear introducing you to the "Recover Gamertag" feature.
Choose "Recover Gamertag" again, and then allow the console to exit the session by selecting "Yes" when prompted to close the introduction menu and launch the recovery process.
Select the "Gamertag" field, and type in the gamertag you wish to recover. Select "Next" to advance to the next prompt.
Enter your Windows LIVE ID and password linked to your gamertag into the corresponding fields on the resulting prompt. A "Sign-in" button will appear after you enter this information.
Choose "Sign-in" to have the console recover the gamertag and download all of its data.