Quartz watches are powered by a battery that sends electric currents through a quartz crystal. They typically need only minimal care, aside from changing the battery when it dies. It is recommended you change the battery soon, if not immediately after it stops to lessen the chance of battery acid leakage, which can cause major damage to the movement.
When the watch is not in use, it is NOT recommended to pull out the stem and crown (the part you use to change the time). Typically, as long as it remains closed, most watches will be dust proof. If the crown screws down on your watch, check it periodically, especially before getting it wet, to ensure that it is screwed closed snugly, to prevent water leakage. If even a small amount of water, dust or debris gets inside into the movement, it can damage the mechanisms. On that note, keep in mind that some watches are not resistant to water at all and are only dust proof. If the watch is water proof, or more likely, water resistant, it is a good idea to have the gasket in the back of the case changed when you have the battery changed. Most watches are not totally water proof, but very little bit helps. Some can only withstand a small, accidental splash of water when washing your hands, while others can be used in the shower or even while swimming. It is best to refer to your owner’s manual for recommendations for your particular model watch as to what would be safe for it, water-wise.
If your crystal (the clear glass-like piece covering the front) becomes scratched, cracked, broken, or shattered, it is a good idea to have it replaced to ensure no crystal fragments end up inside the movement (causing gear damage) and that no other dust or debris can find their way in either.