Turn off the water to the faucet from inside the house -- usually in the basement. Turn the faucet on to allow remaining water in the pipe to drain, and to check that there is no further water flow.
Unscrew the nut that holds the valve assembly in place, usually just after the twist handle. Use an adjustable wrench to get a firm grip and turn the large nut counter-clockwise until it loosens and you can unscrew it.
Remove the valve assembly from the plumbing. Look at the inner end of the assembly for the small screw holding everything together. Use a small screwdriver to remove it; depending on the manufacturer and the age of the faucet, this may require either a slotted or a Phillips screwdriver.
Pry the old washer off with a small eyeglass screwdriver or the tip of a pocketknife. Take the old washer with you when you go shopping so you can get an exact replica to fit your faucet.
Apply a small amount of plumber's grease to the washer on both sides. Slide the new washer in place and replace the screw holding the assembly together. Place the valve assembly back on the stem sticking out of the wall and twist the nut to hold it together. Tighten the nut with the adjustable wrench until snug.