How to Fix a Leaky Faucet
To fix your leaking faucet, turn the pipes below the sink to turn off the water and plug the drain with a rag. If you have a faucet with 2 handles for hot and cold, remove each handle, remove the nut with a wrench, pull out the stem, and replace the seat washer to fix the leak. If you have a ball faucet, unscrew the handle and use pliers to take off the cap and collar. Install new O-rings, springs, valve seats, and washers from a ball faucet replacement kit.
Turn off the water to your faucet. Look underneath your sink for the pipes that run up. Along those pipes somewhere will be handles that you can turn to shut off the water to your sink. Twist clockwise to shut off. Plug the drain. Use a sink plug if you have one or a rag. Nothing will ruin your day faster than having a screw or a washer go down the drain. Determine what type of faucet you have. A compression faucet has two screw handles , one for hot and one for cold, and is the easiest to recognize by sight. The other three types of faucet all have one central, swiveling arm that you can swing from hot to cold as desired. You may have to take your faucet apart before you know which is which, because the internal mechanisms at the base of their arms are all different: A ball faucet contains a ball bearing. A cartridge faucet contains a cartridge. The materials of the cartridge will vary, but handle often has a decorative cap. A ceramic-disk faucet contains a ceramic cylinder. Remove each handle. Pry off the decorative cap if necessary (usually reading “Hot” or “Cold”), unscrew, and remove the handle. Use a wrench to remove the nut. Underneath, you will find the stem, which sits on top of the O-ring, which sits on top of a seat washer. The seat washer is usually made of rubber, which can get worn out after a while. If your faucet is dripping, this is mostly likely the culprit. Pull out the stem. This will expose the O-ring, which will be thinner, and seat washer, which will be thicker. If the handles are leaky (as opposed to the faucet), replace the O-ring. Take the old one to the hardware store and use it to find a replacement. Remove the seat washer. This will be held in place with an upside-down brass screw. Replace the seat washer. Since these washers vary in size, you might need to bring the old one in with you to a parts store to find an exact match. Coat the replacement in plumber's grease before installing it. Reassemble each handle. Any minor leaks should now be fixed. Buy a replacement kit. Ball faucets have several parts that will need to be replaced and some that require special tools. You won't need to replace the entire faucet, just the faucet cam assembly. All of the stuff you'll need, including tools, should be included in this type of kit that runs about $20 and is available in the plumbing section of most home repair shops. Start by unscrewing and removing the handle. Lift off the handle and place it aside. Use pliers to remove the cap and collar. Also, loosen the faucet cam by using the tool provided in your replacement kit for this purpose. Remove the faucet cam, washer, and ball. This will look like a "ball and socket" joint in your body--a movable (usually white) rubber ball plugs the socket, stopping up the water and releasing it. Remove the inlet seals and springs. To do this, you will need to reach into the mechanism itself, probably using needle-nose pliers. Replace the O-rings. Cut off the old ones and coat the new ones in plumber's grease before installing. Install new springs, valve seats, and cam washers. These should all be included in your kit, and should be essentially the reverse of the process you completed. Reassemble the handle. The leak should now be repaired. Remove the handle. Pry off the decorative cap if necessary, unscrew, and remove the handle by tilting it backwards. Remove the retaining clip if necessary. This is a circular, threaded piece (usually plastic) that sometimes holds the cartridge in place and can be pulled out with pliers. Pull the cartridge so that it stands straight up. This is the position the cartridge sits in when the water is on full blast. Remove the faucet spout. Set aside and locate the O-rings. Replace the O-rings. Cut off the old ones using a utility knife and coat the new ones in plumber's grease before installing them. Reassemble the handle. The leak should now be repaired. Remove the escutcheon cap. After unscrewing and removing the handle, locate the escutcheon, which sits directly beneath the handle and is usually made of metal. Unscrew and remove the disk cylinder. This will expose several neoprene seals on the underside. Pry out the seals and clean the cylinders. White vinegar would work well for this purpose, especially if you have hard water. Soak them for several hours to work out the build-up and then assess whether or not they're reusable. Replace the seals if necessary. If they look pitted, frayed, thin, or otherwise worn – or if you simply want to play it safe – bring them into the hardware store to find exact replacements. Reassemble the handle and very slowly turn the water on. Running the water too forcefully can crack the ceramic disk. 
Turn off the water to your faucet. Plug the drain. Determine what type of faucet you have. Remove each handle. Use a wrench to remove the nut. Pull out the stem. Remove the seat washer. Replace the seat washer. Reassemble each handle. Buy a replacement kit. Start by unscrewing and removing the handle. Use pliers to remove the cap and collar. Remove the inlet seals and springs. Replace the O-rings. Install new springs, valve seats, and cam washers. Reassemble the handle. Remove the handle. Remove the retaining clip if necessary. Pull the cartridge so that it stands straight up. Remove the faucet spout. Replace the O-rings. Reassemble the handle. Remove the escutcheon cap. Unscrew and remove the disk cylinder. Pry out the seals and clean the cylinders. Replace the seals if necessary. Reassemble the handle and very slowly turn the water on. 