Brass is an alloy of copper and zinc and will naturally tarnish when exposed to oxygen. Oils from your skin and the oxygen in the air are what accelerate tarnishing. Some people prefer the patina of tarnished brass, but if you want to get the high shine of new brass then it is simple to do with typical household products.

If the tarnish is not too pervasive take about 2 tablespoons of baking soda and add drops of lemon juice until a paste is formed. Apply the paste to your piece and scrub with an old toothbrush. Let it sit in the paste for about 30 minutes and then rinse with water and dry 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. 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.

 If you want to slow the tarnish process, you may want to lacquer it with a clear coat of nail polish, as an added method of protection. Or if you don't want to use lacquer, olive oil is a good compromise. Brass will look brighter and require less polishing if rubbed with a cloth moistened with olive oil after each polishing. The oil naturally retards tarnish.