How to Clean Brass
The technique for how to clean brass is similar for the one used to clean copper. In fact, brass is an alloy of copper and zinc so this is not surprising.
Is it Brass?
Before learning how to clean brass, you should determine that indeed what you have is solid brass and not another metal that has a thin coating of brass applied to it. A simple test is that a magnet will not adhere to brass. If a magnet adheres to your object, there is another ferrous metal underneath the brass layer, which may be quite thin. Caution should be exercised in cleaning this thin layer.
Of course you may have a non-ferrous metal coated with brass and the only way to test if such is the case is by scratching the surface in an inconspicuous location with a sharp knife. If you see yellow underneath it's probably solid brass, if not, treat the object delicately as it is only brass plated.
Most brass you'll find in use in your home these days is covered with a lacquer coating. Unlike the case with copper pots, where you might want to remove this lacquer coating, it's best to leave it on your brass as it protects it from tarnishing. If you regularly dust and clean lacquered brass, it should stay tarnish free.
Over time, however even lacquered brass may tarnish as the lacquer ages. If you want to remove this tarnish, you'll need to remove the lacquer coating, clean and polish, and then relacquer (if you want the continued protection of lacquer).
To remove the lacquer, you'll need to use a commercial lacquer remover or you can try soaking the item in a solution of baking soda and boiling water (1 tablespoon baking soda per quart of water) for about 15 minutes. The lacquer will lift off and you can peel it away.
Once you have an unfinished brass item, there are a number of homemade brass cleaners that can help you remove tarnish. The advantage of these is that they use all natural ingredients, making them easy on you and the environment. Otherwise you can use a commercial product - there are any number of reliable brass cleaning products available.
Tried and True
Here's a product that's stood the test of time and is still very popular. Brasso Multi Purpose Metal Polish cleans brass as well as chrome, zinc or pewter without scratching or leaving a film. They claim it contains no "injurious" chemicals.
Now that you have thoroughly cleaned and polished your brass, you may want to apply another coating of lacquer to protect it from further tarnishing. Even when lacquered, be sure to regularly dust and wipe the brass, to keep it shiny and pretty. This will extend the effectiveness of the lacquer.