A burnt stainless steel pan can be cleaned through a process of boiling and washing using vinegar, water, baking soda and something to scrub the bottom of the pan with.
First, place the pan on a stove and fill the bottom with water. Then add in a cup of vinegar and bring the liquid to a boil. Let the liquid boil for a time or until a substantial amount of the water and vinegar mixture has boiled away. Once the pan has been removed from the stove, add in two tablespoons of baking soda. There should be a considerable amount of bubbles and foam as the baking soda reacts with the vinegar in the water. Once the baking soda and vinegar have had time to react, empty the liquid into the sink and begin scouring the bottom of the pan with a sponge or mesh cloth.
This should remove the burnt stains from the bottom of the pan. If the stains remain after this process, mix a paste with baking soda and a few drops of water. This paste should then be applied to the bottom of the pan and left alone for a time. After the paste has set, return to the pan and repeat the scrubbing process.