1. Shine silver. Tarnish is the enemy, and here are your weapons: For items that are merely dull, filmy or starting to discolor, mix a few drops of mild dish soap with warm water and dip in a soft cloth. Rub the jewelry, then rinse in cool water and buff with a cloth until dry. For heavier tarnish, mix a paste of three parts baking soda to one part water. Wet the silver and apply the cleaner with a soft, lint-free cloth (not paper towels, which can scratch).