Instructions
Power on the console with a controller attached and insert your game disc into the drive.
Go to the Xbox 360 dashboard by pressing the center logo button on your controller. Usually the game boots up right away, so you&'ll need to manually get back to the Xbox 360 dashboard.
Scroll down to the "My Xbox" menu, then scroll over to the right until you reach the "Game Library" option. Press the "A" button on your controller to select it.
Find your game on the menu that pops up and select it with the "Y" button, then highlight and select "Install to Hard Drive" with the "A" button. The console will then rip the game to your hard drive, a process that can take several minutes. Once finished, every time you play the game your console will read the information off the hard drive instead of the disc.