Fix a Scratched CD
As long as the foil on a CD is not harmed, it is theoretically possible to play the CD. Before you start working on a skipping CD, make sure the problem isn't just with your CD player. You can clean the lense of your player with a Q-tip and some rubbing alchohol. Make sure you don't get any of the rubbing alchohol any place but on the lense. Exercize caution if your CD player is inordinately expensive. Try this at your own risk. But if it won't play anything or skips repeatedly on on a CD that every other player does fine with, a dirty lense may be the culprit.
Now take a moment to check your sanity to make sure your CD isn't all covered with gunk. If you've got hot chocolate dried on to it, duh, of course it's skipping. Clean it off and consider embracing sobriety. Your disk is fine.
So if you've made sure that your CD is actually hosed, or you can see huge scratches on the surface, we can get down to fixing it. Cds can have "good" scratches and bad scratches. A bad scratch is one that throws off the laser tracking. You will not have troubles from CDs for any other reason besides the foil being damaged or the laser tracking being thrown off.
Bad scratches run perpendicular to the radius. Don't worry if you slept through geometry class, the red horizontal line in the picture is an example of a bad scratch. The laser is running along, trying to follow the "groove" of information on your disk (think of record grooves) and it runs into this scratch and starts following it instead of keeping on it's circular path. The cd player realizes something is wrong and tries to snap the laser back into the path where it belongs. This is skipping. Skipping is bad.
"Good" scratches run along the radius. The laser is spinning along, comes to a good scratch and might have some trouble reading a few bits of information, but doesn't get confused about where it is headed and continues on it's merry way. Those few bits it can't see are nothing to lose sleep about. CDs are created with checksums, so often the player can figure out what it missed. If it can't figure it out, it will make a guess. The chances of you ever hearing this are very very low. The only thing you should worry about is skipping. Besides, if your disk won't play anyway, because it's skipping all over the place, then you don't have a lot to lose by rendering one sample (out of 44100 per second) indecipherable.
The trick to reparing a CD is to replace all the bad scratches with good scratches. Head to the bathroom. Rinse off your disk with some water. Hot or cold doesn't matter. Now get some toothpaste on your finger. You need the white scratchy kind, not that gell stuff. It has to be abrasive. Locate the section of disk containing bad scratches. What you want to do is run your finger along the radius of the disk over the bad scratch. You need to score deeper than the bad scratch. As long as you're not hitting foil, you're fine. So run your finger along the radius a bit. Turn the disk slightly. Repeat. Rinse off the toothpaste with more water. Dry the Cd with a soft cloth or a bath towel or waterver, again, running the towel along the radius. Pop that disk into a CD player and see if it's gotten better. You may need to repeat this procedure a few times, especially, if the scratches are gouged in.