Take a clean soft, cloth and apply some toothpaste to it.
Rub the product on the cloth in a radial motion over the CD’s surface (you might have to apply more pressure over the scratched surface to help in smoothing out the scratches). Continue this process until most of the scratches are removed. You may find that you need to add more toothpaste during this process.
Clean the CD with water when finished buffing out the scratches. Then take another clean, soft cloth and dry the CD.
Test the CD in a computer or CD player when finished.