If you have a cartridge-type faucet, a leak usually indicates that the O-rings need to be replaced. This is a simple repair that even the novice do-it-yourselfer can perform. If the faucet leaks from the handle, the upper O-ring probably needs replacement, while a drip from the spout will indicate a problem with the O-ring at the base of the spout assembly. O-rings also form a seal between the hot and cold supply lines, so be sure to examine these once you have the faucet disassembled. When replacing O-rings give them a light coating of heatproof lubricant. If replacing O-rings doesn't solve your problems, you may need to replace the cartridge itself.
A ceramic disk faucet that leaks at the base of the handle means that one or more of the inlet seals on the cartridge may need replacing. These seals can be easily replaced. You may also want to clean the inlet ports on this type of faucet since they can become clogged with mineral deposits. A complete cartridge replacement may be needed if leaking problems persist.
A rotating ball faucet is difficult to repair because of its many parts. You should first disassemble the cam, ball, and spout to see if there are any problems there - many leaks result from a worn-out ball or gasket. If those seem fine, remove seals and springs to check for blockages. Leaks also can spring from around the handle or from under the base of the spout. Handle leaks indicate that the adjusting ring has loosened or the seal above the ball is worn. Leaks from under the spout result from O-ring failure. Examine all O-rings encircling the body of the faucet to see if they look worn.