Wash the aluminum pans as you normally would to remove any debris, such as stuck-on food, from the cookware.
Mix 2 tablespoons of cream of tartar with 1 quart of water. Pour the mixture into the pans and bring to a boil on a stove top for 10 minutes.
Remove the aluminum pans from the heat and let cool. Scrub the pans with a clean sponge until you have removed the oxidization and brightened the aluminum. Continue if the pans are still dull.
Pour water into the pan 1 cup at a time until the oxidization is covered. Add 1 teaspoon of white vinegar per every cup of water to the pan. Mix with a spoon.
Bring the vinegar-water mixture to a boil on a stove set to medium heat. Let the mixture boil for several minutes. Remove the pan from the stove and immediately rinse with cold water.
Wash the aluminum pans clean with warm, soapy water. Rinse with cold water and towel dry.