Wash the aluminum pan thoroughly with hot, soapy water and a sponge. Remove all food particles and grease. Use a scrub brush if you have trouble removing stubborn, cooked-on food.
Fill the aluminum pan with water. Add a cup of vinegar. Cut a large lemon into slices, and add it to the pan.
Put the aluminum pan on a stove burner, and turn the heat to the highest setting. Let the water boil for 20 minutes.
Scrub tarnish with a salt-coated lemon slice, if the boiling vinegar solution did not fully remove it. Wash the pan again with hot water and soap.
Dry the aluminum pan with a soft towel each time you wash it, to keep tarnish from returning.