Create a mixture of 1/2 tablespoon of mild liquid dish soap and 3 cups of distilled water. Stir to mix the mild detergent, which contains no dyes or perfumes, into the water.
Dampen a soft cloth with the mixture, and wipe down the stainless steel, applying pressure if necessary. If the hard water stains persist, continue on to the next step.
Create a paste with 1/2 cup of baking soda and 1/4 cup of white vinegar. Stir the ingredients and add more baking soda, if necessary, to thicken the paste.
Spread a thin layer of the paste directly onto the difficult hard water stains. Allow the paste to remain for five minutes before wiping it away with a damp cloth.
Dampen a separate soft cloth with distilled water, and wipe away any remaining residue. Dry the stainless steel with a soft cloth to prevent water marks and streaks.