It is quite normal for silver to oxidize over time. However, there are several ways to avoid oxidation and to clean your jewelry.
To prevent oxidation of silver jewelry:
Store your silver jewelry in an airtight container or jewelry box to minimize contact with ambient air.
Wear your jewelry, it's the most effective way to prevent oxidation!
To clean your silver jewelry :
Rub your jewelry gently with a jewelry wipe ( available in store! ) to remove traces of oxidation.
Try the good old toothpaste trick. Apply a small dab of toothpaste to a toothbrush. Gently rub your silver jewelry then run it under cold water to remove all traces of toothpaste.
There are also several types of cleaners you can soak your silver jewelry in to remove traces of oxidation. For my part, I avoid this kind of cleaning products which can easily damage the desired oxidation of your jewel, or even the semi-precious stones.