If you happen to have a Family Video, or some sort of rental store nearby, they'll put a disc through their cleaner. Sometimes for a small charge, but a lot of times for free. I brought an old game to them that was scratched to Hell, just as a last resort. I couldn't believe how much their machine was able to clean and polish the disc. It almost looked brand new.
But since rental stores have pretty much all disappeared, I'm guessing that isn't an option for you. So you might try Gamestop, or some sort of used game store. They would probably clean the disc for you, or at the very least, they'll probably tell you what machine/method they use to clean used discs they obtain.