Instructions
Turn on the Xbox 360 console. The game disc you want to make a free backup copy of should be inserted.
Scroll up to the ̶0;My Xbox̶1; section of the Xbox Dashboard. The first icon should say ̶0;Play Game Name̶1; and have a picture of the game. Do not select it.
Press the ̶0;Y̶1; button on the controller with the ̶0;Play Game Name̶1; icon highlighted. This will open a new menu.
Select ̶0;Install Game̶1; from the menu. This is the option to make an Xbox 360 backup. A prompt will appear to select a storage device.
Select the Xbox 360 hard drive. The console will automatically back up the entire game disc to the hard drive. This will take about 10 minutes, depending on the size of the game.