Rinse off the stainless steel surface with water. This will remove dust, dirt and the majority of food stains right away. Though the surface may not look clean yet, it should at least be free of large crumbs and other debris.
Sprinkle baking soda over the slightly damp surface of the stainless steel. Leave the baking soda to sit for 5 to 10 minutes. Scrub the baking soda over the surface with a wet sponge, working with the grain of the steel. Rinse the baking soda off of the surface, and rinse out your sponge.
Apply a small amount of white vinegar to any heat stains on the stainless steel. Rub into the surface with a soft cloth.
Dry the surface with a lint-free cloth or paper towel. If desired, you can add a little more shine by polishing with a small amount of olive oil.