After years of daily use, a faucet may develop a leak around the handle when it is turned on, or drip constantly from the faucet no matter how hard you try to turn it off. Both problems can often be solved by replacing the washer and sealing the valve threads with Teflon tape.
Start by turning off the water, then remove the screw in the handle of the faucet.
Next, pry off the faucet handle. If corrosion has it frozen in place, you may have to use a spray lubricant like WD-40 and slowly work it loose.
After the handle is off, use a deep well socket and wrench to unscrew the valve from the housing.
Once the valve is loose, take it out of the housing.
Remove the screw in the end of the valve, and take out the washer.
Replace the old washer with a new one of the same diameter and thickness and tighten the screw holding it on.
Wrap the housing threads on the outside of the valve with Teflon tape to prevent it from leaking at the handle.
Screw the valve back into the housing, being careful not to strip or over tighten the threads.
Replace the handle, turn on the water, and you should be ready to go.