Spray a nonabrasive cleaner on the porcelain sink. Allow the cleaner to soak into the residue on the sink surface for 10 minutes.
Wipe the sink with a wet sponge, removing the soapy residue. Dry the sink with a dish towel.
Cut a lemon in half with a knife. Rub the lemon over the entire porcelain sink. Squeeze the lemon gently as you rub to release the juice inside. Allow the lemon juice to remain on the sink for 10 minutes. Rinse the sink with cool water and a sponge.
Put the stopper in the drain hole. Pour 1 cup of white vinegar into the sink. Wet a sponge with the vinegar and wipe over the porcelain sink surface. Rinse the vinegar completely from the sink with the sponge and cool water. Dry the sink with a dish towel.