Step 1: The Materials
Get these materials (Usually you'll have them lying around your house):
-Lotion (Of course)
-microfiber cloth (Their very soft. Screen cleaing cloths, and eyeglass cloths are both microfiber. Wanna go cheaper? Take a baby wipe and let it dry for a couple of hours. Boom! Soft polishing cloth)
-You're injured disc. It can be a CD, DVD, video game (including teeny-tiny GameCube ones).
-Something to put under that disc to catch excess lotion, such as toilet paper, a wash cloth, towels, etc.
Step 2: Start the Buffing Process!
First put a little squirt of lotion onto your microfiber cloth, then start buffing from the inside of the disc out, using a little bit of pressure (Not too much; you'll crack the disc!). This is what gets off the heavy, deeper scratches. Do that until the lotion on your cloth runs out.
Next, put another squirt of lotion on, and go around in tiny circles on the surface of the disc, using light pressure. This is what gets off some of the lighter scratches, and polishes the disc. Let the lotion dry on the disc when you've finished (Usually after you run out of lotion on your cloth). After it's dry, go around in small circles again with a dry microfiber cloth until all the dried lotion is removed
If there is still some greasy residue left behind, you can run it under some water in the sink, or even give it the old spit 'n shine.... Or not.
EDIT: Read this before you begin buffing!!! To avoid greasy build-up on your discs all together, you can dilute the lotion with 1 part water to every 3 parts lotion. This makes the lotion so that it doesn't leave your CD's slightly cloudy after. Sure, the cloudyness shouldn't afftect the way your disc plays, but it makes the disc look less.......Fixed? Working?