Dampen a soft cloth with warm water, and add 3 or 4 drops of dish soap to the cloth. Wipe the stainless steel cooktop in the direction of the grain, and allow the soapy solution to soak for two or three minutes to loosen any stains.
Wipe the stainless steel cooktop with the soapy cloth to remove any residue. If any stains remain, wipe the cooktop with a damp nonabrasive scrub pad.
Sprinkle a liberal amount of nonabrasive powder cleanser on any remaining stains. Scrub the gas cooktop thoroughly in the direction of the grain.
Rinse the cooktop thoroughly with a clean, damp cloth.
Dry the gas cooktop with a soft microfiber cloth. If the stainless steel cooktop looks dull after cleaning, use a polish to restore its shine.
Apply a small amount of stainless steel polish to a soft cloth. Apply the polish to the cooktop according to the manufacturer directions.
Buff the stainless steel cooktop in the direction of the grain with a clean, dry cloth.