Fill your sink with warm water and add a little bit of dish detergent. One small squirt of detergent is all you need.
Dip the disk in the water and gently move it around. Be careful not to hit the sides of the sink with the disk. Repeat the process if any stubborn dirt remains.
Rinse the disk by holding it under warm, running water. Make sure all the dirt and soap is removed. Let the disk air dry with the label side down, or dry it gently with a soft cloth.
Put a small amount of white, "chalky" toothpaste on the disk and gently rub it in using a circular motion. You must use a white toothpaste; gel toothpastes won't work.
Leave the toothpaste on the disk for five minutes
Hold the disk under warm running water to remove all the toothpaste. Set the disk aside (again, label side down) and let it air dry. You can also dry the disk by wiping it gently with a soft cloth.
Note: You must clean the disc before polishing it with toothpaste; this prevents dirt from being rubbed into the disc. Dirt that is rubbed into the disc can cause more scratches.
Warning: Badly scratched disks may not be repairable.