A simple, homemade paste of vinegar, salt and flour, and a lot of elbow grease, can remove tarnish from brass. Any mild acid and abrasive will work, so lemon juice can be used instead of vinegar and cream of tartar or baking soda can be used instead of salt. There are also a number of commercial brass cleaners and polishes available.
Brass items can be made of either solid brass or brass-plated steel. A magnet will stick to brass-plate but not solid brass.
Any removal of tarnish also removes some of the brass, so more care must be taken with brass-plated items. They should never be cleaned with a highly abrasive cleaner or scrubbed with an abrasive scrubber such as steel wool. Solid brass can withstand a more vigorous scrubbing and a more abrasive cleaner. Once the tarnish is removed from the brass, it can be polished with a commercial brass polish to preserve the patina.
Often, both solid brass and brass-plated items are lacquered to reduce the need for frequent polishing. Lacquered brass should only be cleaned with a mild detergent. Ammonia-based cleaners will harm the lacquer coating. After lacquered brass is cleaned, it should be wiped with lacquer thinner to remove all traces of cleaner. Seriously damaged lacquered brass can have the lacquer removed and reapplied.