I've discovered several methods online today to clean a burnt pan:
1. From Pioneer Thinking: slice up an onion put it in the pan and add enough water to cover the burnt part, put on the stove and heat until the water is boiling, then take off and leave to cool. Let it stand for a few hours, the black should then come off fairly easily.
2. From Ehow.com: Wash away as much of the food as possible, using cold water for eggs, chocolate and starch-based foods. Fill the pot with water. Add 1 to 2 tsp. dishwashing liquid and bring to a boil. Simmer for 10 minutes, then cover the pot, turn off the heat and leave the pot to soak for 30 minutes. With a wooden spoon, scrape away as much of the burned food as possible. Rinse well. If burned areas still remain, cover them completely with a generous amount of baking soda. Drizzle in just enough water to create a thick paste, smearing the paste up the sides of the pot if needed. Set aside for at least 4 hours, preferably overnight. Without rinsing the pot, add 3 parts water to 1 part distilled vinegar to cover the burned food by at least 2 inches (5 cm). Boil for 10 minutes and then leave overnight. Repeat steps 2 through 5 as needed.
3. From ThrifyFun: Put hot water in the pan along with some vinegar and let it sit overnight. This also works well with cleaning your stove top burner pans.