Hand wash with gentle dish soap and dry with a soft towel. To polish a copper mug mix 3 parts baking soda with 1 part vinegar. Using a sponge apply the mixture to the mug. Let sit for 10 minutes. Rub with the sponge and rinse with warm water drying with a soft towel. You can also use half a lemon and some table salt. Sprinkle the table salt on the lemon half then rub directly on the mug. Rinse, wash, and hand dry.