Wipe loose food crumbs off the stainless steel cooktop with a damp paper towel. Discard the paper towels.
Pour 2 cups of warm water into a bowl. Add 1 tablespoon of ammonia to the water.
Wet a clean cloth with the ammonia mixture and wring out excess moisture. Lay the cloth over the remaining food stains for 5 to 10 minutes to loosen the stains. Wipe the loosened food stains off the cooktop with the cloth.
Moisten a nylon mesh scrubber with white vinegar. Sprinkle baking soda over the scrubber to cover one side.
Scrub remaining food stains off the cooktop with the vinegar and baking soda mixture. Rinse the surface by wiping it off with a damp cloth. Dry the stainless steel with another clean cloth.
Pour a quarter-sized amount of olive oil onto a clean, dry cloth. Buff the stainless steel cooktop with the oil to give it a luster and to keep stains from sticking easily.