CD - DVD Cleaning tips.

Without proper storage your CDs may get scratched or dirty. It is always recommended that discs are put back in the jewel case after use, but that is not always possible. At $15.00 (music) to $60.00 (video games) it is not worth having to buy new media every time you receive a disc read error. There are fix-it kits available, but this is the poor person's guide. For about $.99 you will be able to clean up most problems.

Scratches.

Scratches are usually the #1 problem. When purchasing used media be on the look-out for tell-tale signs of use.
Discs that have scratches that run circular around the discs should be avoided. These are the ones that really screw up data reading. Scratches that run from the center to the edge of the disc are less problematic, but may still pose a problem. Check the store return policy before purchase.
Scratches on the upside (the painted side) are also a real problem. If you can see through the disc - it will not play that area.

Remedy: Scratches.

There are kits that will fix this problem, such as skins or disc doctors. The skins provide a layer that helps the lens read past the scratch and are never 100% reliable.
Another method is the Disc Doctor that grinds down a layer of plastic to reduce the size of the scratch. Also not 100% reliable (and costly).
If your disc is scratched on the paint side, it is possible to paint over that area with some sort of opaque substance such as white out or nail polish. When applying these, be sure to not put it on too thick. This could upset the balance of the disc as it spins.

Remedy: Dirt, Fingerprints and Grime.

It is important when cleaning your discs that you do not create a greater problem. Wiping dirt off can create scratches. I use warm water to start with. Letting it run over the media side for 30 seconds or less. Using hot water may damage the painted side.
Use a clean, soft cotton cloth to wipe the residue away. I use an old t-shirt for this.
Always wipe from the center of the disc to the outside edge. Never wipe in a circular motion and do not apply too much pressure.
If water does not solve the problem, you may want to use isopropyl (rubbing) alcohol. Put some rubbing alcohol on your rag (clean t-shirt) and wipe as instructed above. Be sure to not get any alcohol on the painted side, as it may damage the surface. This proves to get rid of soda, beer, gravy (don't ask) and that gum companies seal disc packs with.
I have had a problem with Official Playstation Magazine demo discs and the glue they use to seal their packages. This method works pretty well.