Wet a nylon mesh sponge with full-strength white vinegar. Scrub the stainless steel cooktop to moisten the stains and discoloration. Allow the vinegar to sit on the surface for two to three minutes.
Sprinkle the sponge with baking soda. Gently scrub the vinegar-moistened stains and discoloration on the surface of your stainless steel stove.
Wipe the loosened stains and baking soda off the stove top with a damp cloth.
Treat any stubborn or burned-on stains with a weak ammonia solution. Dampen a clean cloth with water. Add five to 10 drops of ammonia to the moist cloth. Scrub the remaining stains and discoloration with the ammonia solution.
Dry your stainless steel stove top with another cloth.