Add enough water to your pot to cover the burned and stained area. Place on the stove top and set to high. Remember to be careful while working around the stove as you should observe all the necessary safety precautions.
Add a 1/2 cup of baking soda to the pot and bring to a boil. The baking soda will help loosen up the burnt areas on the bottom of the pot. Depending on the size of the pot you may want to add more baking soda for it to be effective.
Allow the solution to boil until the blackened and charred stain begins to disappear. Continue boiling until the stained area is completely gone. If some of the stain still remains, move to the next step. Be careful while the water boils as you do not want to get burned.
Drain the pot and place it in your sink. Add enough dishwasher detergent to cover the remaining stained area. Add 1" of boiling water and allow the pot to sit overnight.
In the morning, rinse the pot and the remaining stains should be gone with some gentle rubbing. Remember not to scrub too hard as you do not want to damage your pot.
You will also find a wide variety of different cleaning solutions that are designed specifically for the purpose of removing burnt stains from pots. Most of these cleaners are readily available at any convenient store. The basic premise is that you spray the solution on the pot and it will begin to create a thick foam. Then you let it sit for a few minutes. The foam will loosen the burnt out stains and then all you have to do is rinse the pot to clean it. Most of these cleaners do not require any tedious scrubbing.