Trumpet mouthpieces, commonly made of silver or silver plate, can tarnish or oxidize easily. Cleaning this oxidization off of the mouthpiece's surface can be done cheaply and easily by following a few simple steps. Just because the mouthpiece is tarnished does not mean you need to replace or dispose of it. Bringing your mouthpiece back to its original shiny, clean state can be accomplished using common materials.
Cover a soup-type bowl in aluminum foil.
Add 1 tbsp. of salt and 1 tbsp. of baking powder to the bowl.
Pour some hot, but not boiling, water into the bowl and stir.
Submerse the trumpet's mouthpiece in the mixture. Allow three to five minutes for the mixture to remove the layer of tarnish on the mouthpiece. Polish the mouthpiece using a cloth and the dry-ingredient mixture. Repeat Steps 1 to 3 if the mouthpiece is severely tarnished.
Do not polish the mouthpiece too hard if it is known to be silver-plated, as some of the plating can be removed if polished too vigorously.