Add hot water to a clean sink. Pour 1 tablespoon of liquid dish soap to the water, and mix until suds form. Submerge the aluminum in the water, and then wash it with a cloth.
Rinse the soapy mixture off the aluminum with cold water. Pour 1/2 quart of lukewarm water into the aluminum cookware. Add 1 tablespoons of cream of tartar. Increase the mixture for large cookware.
Stir the water and cream of tartar with a spoon. Set the cookware on the stove, and bring the mixture to a boil. Allow the mixture to boil for 10 minutes. Remove the cookware from the stove and discard the mixture. Continue with the remaining steps if the darkening remains.
Fill the aluminum pot with water 1 cup at a time. Mix 1 teaspoon of vinegar for every cup of water added.
Boil the mixture on the stove for several minutes. Discard the mixture immediately, and rinse the aluminum with cool water.
Wash the aluminum cookware as you normally would, and then dry it with a soft towel.