A leaky valve usually is the reason for replacing valve stem packing, which often is made of graphite. The packing is wound around a valve stem inside a packing nut to hold it in place. Turning the packing nut with a wrench usually will stop leaks by compressing the packing inside the valve and expanding the seal. Once the packing is worn, however, it must be replaced. Packing material is sold at hardware stores.
Removing the Valve Assembly
Shut off water supply to the leaking valve, which typically is found under the home. The pipe you're working with will be connected to another pipe that supplies it with water.
Once the water is shut off, turn the valve you're working on to the left until it is all the way open.
Put a pipe wrench on the body of the valve to hold it and an adjustable wrench between the packing nut and spout. Turn the adjustable wrench left.
Remove the valve assembly from the faucet.
Remove the retainer nut from the faucet handle with a socket wrench and take off the handle.
Replacing the Packing
Unscrew and remove the packing nut. Use a screwdriver to pry out old packing string from the packing nut.
Replace the packing string with string of the same size. Replace the packing nut and tighten it firmly.
Replace the faucet handle with the socket wrench.
Replace the valve assembly and tighten it with the adjustable wrench, holding the valve body in place with the pipe wrench.
Turn on the water supply to test the faucet for leaks. If necessary, tighten the packing more.