Soak the copper in white vinegar. White vinegar is a mild acid that will eat away the alkaline tarnish. White vinegar is also a disinfectant.
Sprinkle salt over the wet copper. The salt will adhere to the copper and it act as a mild scouring powder to help work away the tarnish.
Scrub the salt into the tarnished areas on the copper with a cloth or an old toothbrush. Work until the tarnish is gone and the copper is clean.
Rinse the copper and dry it with a clean cloth.
Apply a dime-sized amount of ketchup to a clean cloth.
Rub the ketchup into the copper to polish it.
Buff the ketchup off with another clean cloth. Buff until the copper is bright and polished completely.