dripping faucets are almost always the result of a warn out fauget washer, a rubber part that seals the water when it is shut off.
Replacing it is very easy.
1) Turn off the water. If this is a sink, there is almost always a valve under the sink you can shut off to kill the water to the sink.
2)Open the tap up completely to make sure you have the water off.
3) Take the tap apart. This is different for different valve systems, such as systems that have only one handle. For a two handle system, you want to take the part out that the handle is attached to. this is called the valve stem. It is usually removed by unscrewing a large net at the handle base.
4) On the bottom end of the valve stem, is a piece of rubber typically attached with a single screw. Take the whole stem with you to the hardware store so they can give you the right facett washer replacement.
5) Remove the old facett washer, and install the new one.
6) Reassemble, and turn back on the water.
BTY, it is usually smart to replace both facett washers at the same time, as they usually wear out about the same time.
If you can not manage to cope with doing this chore, try replacing the whole facett. That is even easyer. It is cheaper to replace the whole facett, than to call a plumber.
1. turn the water off
2. take the knob off the faucet and any bolts hold it down underneath the knob.
3. pull suspected crummy washer out of its little hole.
4. take to home depot/lowes and match it up. Pay 2 $
5. Put it all back together and enjoy life drip free.
6. repeat for the other knob :)