Soak a clean cotton cloth in warm soapy water, and wring it out. Rub the stainless steel appliance with the damp cloth. Dampen another clean cotton cloth with white vinegar. Rub the appliance with this cloth until the fingerprints have disappeared.
Apply a small amount of commercial stainless steel cleaner to a clean, dry, cotton cloth. Follow the manufacturer's directions for use. Rub the cleaner into the appliance with the grain of the steel.
Mix half a cup of baking soda with a few squirts of liquid soap or detergent. Apply the paste to a nylon scouring pad. Scrub the appliance with the pad. Wipe the baking soda off the appliance with a clean, damp cloth.