Use an air duster on the CD to get rid of any dust that may have settled or stuck to the surface of the DVD, and then use a soft cloth to wipe any smudges off the disc softly. Do this before you use any sort of solution.
Clean a DVD with either water, a store-bought DVD cleaner or a gentle solvent in your home. You can start with just rinsing, or if you can plainly see dirt or some substance on the DVD surface, you should surpass the water and actually use a mixture of cleaners. Substances you can use are a very mild dish detergent, hand soap and water, equal parts rubbing alcohol and water, glass cleaner such as Windex for substances such as soda, mild shampoo such as baby shampoo and lukewarm water for sticky substances, alcohol, methanol, ethanol, mineral water, lens cleaner, or water-based detergents mixed with water.
Hold the DVD on either edge and insert your finger through the middle hole. Make sure to never touch the silver shiny part of the DVD. Dip a soft cloth into the cleaner and apply it to the shiny part of the DVD.
Use the soft cloth to rub cleaner solution into and around the DVD surface. Start at the center and rub straight outward in a back and forth manner. Never rub in a circular motion. Make sure you remove any fingerprints, dust, dirt, oil or sticky residue. Do this until the DVD surface is dry and clean. Place back into its case to protect it in the future.
Bring the DVD to an electronics store to get it repaired if it still is damaged after cleaning it, as there may be some scratches that you cannot remove without special treatment.