Things You'll Need
Instructions
Insert the game into your Xbox 360.
Download the New Xbox Experience, or NXE, dashboard update if you do not have it. Log into Xbox LIVE and allowing your console to automatically download it.
Allow your console to restart when prompted after the dashboard updates and exit to the dashboard if necessary.
Scroll up or down to the "My Xbox" section of the dashboard, where you view title art of the game currently in your disc drive.
Press "Y" to open a new page.
Go to "Install to hard drive" and press "A." Either your console will begin backing up the game to the hard drive or you will be prompted to add space to your hard drive by deleting items. If the latter occurs, clear enough space off your hard drive to allow the game to save.
Complete the backup process by pressing "A" when the game finishes saving.