Place the video game disk under clean running water. Don't rub it dry. As the water runs off, you should be able to locate the scratches.
Place a dab of toothpaste on the video game disc. Use the simplest toothpaste possible, without any gels or additives. Use your finger to spread the toothpaste over the entire video game disc, rubbing in a circular motion and concentrating on the area where the scratches are. This motion buffs out the scratches.
Set the video game disc down to dry. After it's dry to the touch, which should take about 10 minutes, wash the toothpaste off gently under clean running water. Dry the disc with a clean, soft cloth.