Brass is an alloy of copper and zinc and will naturally tarnish when exposed to oxygen. Some people like the patina of tarnished brass and the tarnish is actually a protective layer for the brass, but if you want to get the shine of the new brass it's pretty easy to do with some typical household products.
If the tarnish isn't too pervasive take about 2 tablespoons of baking soda and add a few drops of lemon juice - from concentrate is fine - until you have a nice paste. The lemon juice will bubble and fizz as you add, don't worry it'll stop after a second or two. Take an old toothbrush and apply the paste to your piece and scrub. Let it sit in the paste for about 30 minutes and then rinse it with water and dry it thoroughly.
If the piece is heavily tarnished or the above doesn't work, you can place the piece in vinegar and let it soak for 30-60 minutes and then scrub it with an old toothbrush. Once clean, rinse it with water. This cleaning method is more aggressive and may leave the piece more "raw" looking - it won't have as warm of color until the patina rebuilds.
Oils from your skin and the oxygen in the air are what accelerate tarnishing. If you want to slow the tarnishing process, wipe the piece with a soft cotton rag after wearing and store in a plastic bag with an anti-tarnishing strip.