Soak a clean cloth in white vinegar. Rub the cloth over the hard water stains on the stainless steel until they are gone.
If the spots are very old, hold the cloth over the stain for 10 minutes until it softens. Then buff the stain out with the cloth.
Dip a scrubbing brush in the white vinegar if the stain is still visible. Scrub the stain until it is completely gone.
Apply a dime-size amount of vegetable oil to a clean cloth. Buff the surface of the stainless steel until it is bright and polished. Buff off any excess oil with another clean cloth.