Clean your pan as you normally would with hot soapy water and a sponge. Then, fill it with water and 1 cup of vinegar, and leave it overnight. Clean it again with a scouring pad. If you still have burn marks on your pan, you'll need to use a more aggressive treatment.
Fill your frying pan with water, and then add 2 tablespoons each of baking soda and vinegar. Put the pan on the stove, and heat the water to boiling. While the water is boiling, use a wooden spoon to loosen the burned material at the bottom of the pan. It is important to use a wooden spoon, as a steel utensil will scratch the pan.
Turn the heat off, and pour the contents of the pan down the drain. There will be plenty of dark grainy material in the mix.
Clean the pan as you normally would with a sponge and dish soap. All the burnt material should be gone.