A faucet dripping water can be indicative of a larger problem that could cost you hundreds of dollars. The most common causes for sink faucets leaking include defective parts like o-rings, washers and gaskets. Corrosion and mineral depostis can also lead to sink faucets leaking.
Once you determine the trouble stem you'll need to turn off the water. Next remove the handle with a Philips head screwdriver. So that the stem is visible.