As a jewelry maker and collector, one ubiquitous element that affects my life is oxygen. Discoloration on the surface of many metal alloys is common and called by a variety of names: patina, oxidation, tarnish. These gray, brown, or black surface changes are a result of a chemical reaction between the metal and surrounding compounds. The most common reaction is with oxygen, but tarnish can accelerate as oxygen combines with organic materials such as body oils. When organic materials breaks down in the presence of oxygen, it creates hydrogen sulfide, which is the biggest cause of oxidation on jewelry.
The good news is that the patina is a surface issue only - the reaction will never go deeper into the jewelry. Another piece of good news is that cleaning the tarnish off is often easily done by rubbing the affected surface with a polishing cloth. There are many cloths on the market, but my favorites have a polishing compound embedded in the cloth itself. The cloth picks up the tarnish and leaves the metal surface shiny and bright. You can see in the image below that I have polished one earring of a pair from Chimayo, NM.
Finally, oxidation is sometimes used intentionally as a patina - desired coloration of the metal. So if the color change is aesthetically pleasing to you, you may leave it! I have a few bronze pieces that have turned a lovely reddish-brown over the years, and I haven't yet polished them back. I also like to leave the patina in the recesses of jewelry that has engravings to create contrast.