Combine baking soda with lemon juice to clean copper naturally, or sprinkle just baking soda onto a cloth and polish the tarnished copper.
To keep your copper shiny longer, you can spray or polish a lacquer. Try to keep the oils from your fingers and skin off of the copper, as they can cause discoloration. If you are wearing copper jewelry, apply a clear nail polish to your piece to prevent the copper from coming in contact with your skin.
