Remove any leftover food, sauce and other debris from the stainless cookware and utensils, and place the debris in a trashcan or bag. Rinse off the stainless steel with lukewarm to warm water to remove any caked-on debris. Rinsing also keeps debris from clogging your dishwasher's pipes.
Place cookware on one rack of your dishwasher and place any utensils in a basket alone -- and do not mix stainless steel with silver utensils in the same basket. Staining can occur, as well as a chemical reaction.
Add a mild dish-washing detergent to the appliance, and wash the stainless steel using a regular wash cycle. Do not use an abrasive cleaner or solution to clean your stainless steel. These substances can damage stainless steel. As soon as the cycle is complete, remove the cookware and utensils and dry off any remaining moisture with a clean, soft cloth or rag. Do not put the stainless steel away damp -- this can cause water and rust spots to form on the metal.
For caked-on debris that rinsing and your dishwasher cannot remove, make a paste of equal parts warm water and baking soda and apply it to the matter. Let the paste sit on the soiled part of the stainless steel as long as possible -- overnight is ideal -- then rinse off under warm, running water. Do not use an abrasive scrubber or other tool to break up the debris, as doing so can scratch the stainless steel.