If you're averse to using commercial products to polish your favorite brass pieces, you might find some natural alternatives right in your own kitchen. Some might even surprise you in a good way, because they can restore your brass pieces to their original luster with relative ease. You might not favor the smell of one method -- a cooked onion -- but any objections should peel right away when you see the results.
Moisten a clean cloth with olive oil. Wipe the brass until it shines.
Squirt some ketchup on a clean cloth. Spread it over the surface of the brass. Wipe off the residue with another cloth and buff the brass until it gleams.
Dampen a cloth with Worcestershire sauce. Spread it over the brass piece. Rinse the brass with warm water. Buff the brass to a shine with a microfiber cloth.
Combine 2 tablespoons white vinegar and 2 tablespoons lemon juice in a bowl. For brass that is heavily tarnished, add enough baking soda to create a paste. Rub the solution onto the brass with a soft cloth. Rinse the brass under lukewarm water and then buff dry and then polish with a microfiber cloth.
Chop an onion into large pieces. Place the pieces into a saucepan and cover them with water. Bring the onion pieces to a boil. Use a strainer to separate the onions from the onion water. Dip a soft cloth into the onion water to polish tarnished brass.