How to Recover
In order to recover a gamertag on the Xbox 360, turn on the console. Ensure the console is connected to the Internet and connect a controller. Move to the "My Xbox" list of items, then move to the "Sign In" panel and press "A." Hold the left thumbstick to the right and press "A" on the last tile, named "Recover Gamertag." Press "A" again to begin recovery, then select "Yes" to exit the current session. Press "A" to continue, then enter your Live email address and password. Your account will be downloaded and ready to use shortly.
Offline Achievements
Xbox 360 games allow users to earn achievements for in-game accomplishments even while the console is not connected to the Internet. When connected to the Internet, Xbox Live saves the achievements to your profile on the server. When offline, however, the achievements are recorded only on your memory device. Recovering your gamertag will lose all offline achievements since the last time you signed in on Xbox Live.
Separate Locations
Xbox Live gamertags are only allowed on one console at a time. Though your gamertag will not be deleted from your original memory device or console, the new console or device will become associated with your account. If you recover on a friend's console, for example, you will be required to recover the gamertag again on your own console in order to log in at home.
License Restoration
When content is purchased on an Xbox 360 console, the content is licensed for that console and for the account it was purchased on. For example, if you download a map pack for a game, all users of your console will be able to play the maps. If you then transfer your account to another console, only your profile will be able to use the maps. After recovering a gamertag to a new console, you must restore the licensing for all purchased content so you are able to use it and the new owner of your previous Xbox does not take ownership of the licenses.