This is not a guide on how-to JTAG or RGH your console, there are lots of guides online but I advise you contact a trusted seller and send-in or purchase a pre-modded Xbox 360 system. Note: if your disk is unreadable or just says play game and doesn't work then buy a new one is your only option, but if it reads what the game is you're in luck. All you have to do with a USB (Flash Drive) in order to install JTag software on your Xbox 360 console and play unlimited games free. Once you do it correctly you can just hit play game as you usually would. If you hear it spinning just dashboard then do it again.
Done correctly you won't hear your game spin because it's playing from the installed copy your disk it just confirms you own a legit copy to play the installed disk file from hard drive. It will tell you to insert your disk which you will want to do, but the first time you play the game instead of hitting 'play game' as you usually would, you will need to hit options and then hit play game. This is a copy of the disk, not disk specific which is legal to do and the reason being is you can't just go to the game and play it. You can have your friend install it onto your hard drive or just move it onto a flash drive. You can do this and it is legal as long as you can put your scratched disk in and it tells you what the game is.