Most game stores can re-surface discs. It's a process whereby they replace the entire surface of the disc, rather than simply polishing off the scratches. It's cheap, quick, and effective.

Remember, though - if the scratch is on the label side of the CD/DVD, then the data has been damaged and it cannot be repaired. If it's on the shiny, unlabelled side only, then there's a good chance it can be fixed. No matter how bad the scratches are, re-surfacing will take care of them all, unless they affect the data.

Occasionally, in matters like this, people will say things like "I heard that you can fix it by..." or "This guy told me that it'll always work if you use..."
Whenever you hear something like that, either ignore it, or seek independent verification.

It always puzzles me why people borrow games and then take so little care of them. It's not hard to handle a disc properly, and it's only polite to be careful with something that belongs to someone else... yet still there are dimwits who think that other people's software makes a great frisbee, coaster, paint palette, spatula, or whatever else they do with them. I'm reminded of a time I lent FFIX to a friend. He got the discs filthy by handing the disc surfaces with food on his fingers. He then 'cleaned' my game by rubbing the discs on his carpet. I wasn't impressed.