Instructions
Turn on your Xbox 360 and make sure that you are signed out of any profiles.
Press the "Guide" button -- the big, glowing one in the center of the controller -- and select "Recover Gamertag" from the list of options that appears on your screen.
Enter your Windows Live ID and the password linked to the gamertag you want to recover.
Follow the instructions that appear on your TV screen. The process is mostly automatic, you will simply need to download the information onto your Xbox when prompted.