If you have a leaky faucet, there are two main components that might be the source of the trouble: the valve stem or the faucet washer. The valve stem is the portion of the faucet that regulates the flow of water. The stem attaches to the handle and, by turning the handle, raises or lowers against the faucet seat. At the bottom of the stem is a rubber washer that creates a watertight seal. Stopping a leaky faucet is simply a matter of replacing either one or both of these parts.
Shut off the water for the leaky faucet you want to repair. The faucet and type of installation affect how this is done. For a bathroom or kitchen faucet, the water supply shut-off knob is usually located directly below the faucet, connected by a water supply hose. In this case, rotate the water supply knob clockwise to shut off the water. In other installations, mostly in bathtubs or outdoor faucets, there is not a separate shut-off valve and you have to turn off the water supply for the entire house. The main water supply shut-off valve is usually installed next to the water meter. Rotate the valve with a pair of pliers or wrench to shut off the water.
Remove the faucet handle screw. These are usually hidden underneath the "Hot" or "Cold" faucet labels. Pry off the label with the edge of a sharp knife. Remove the faucet screw with a Phillips screwdriver. Pull the handle straight off. The faucet handle might be held in place with a small screw on the back or underside. If so, remove the screw and pull the handle straight off.
Examine the valve stem and locate the two hexagonal nuts. Unscrew the topmost nut, which is called the packing nut, with the wrench. Pull this off the stem. Remove the second hexagonal nut, which forms the base of the valve stem.
Check the valve stem for cracks or other signs of wear. If you find any damage, you need to replace the stem, as this could be causing the leak.
Turn the stem over so you can examine the rubber washer on the bottom. This also should be replaced if cracked or worn, since a damaged washer definitely causes a leak. Replace it by unscrewing the retention screw with a flat bladed screwdriver. Pull the old washer out and insert the new one. Secure it with the screw.
Lightly dab a coat of silicone grease on the bottom of the washer face. Apply the pipe thread compound to the threads on the stem. Insert the stem into the faucet and tighten with the wrench. Slip the packing nut over the stem and tighten.
Place the faucet handle over the end of the stem. Rotate slowly until you feel it fall into place in the grooves on the top of the stem. Insert the screw and tighten it. Press the screw cap back into place.
Restore the water supply. Run the faucet. Tighten any nuts as necessary.