Shut off the water supply to the faucet. Take out the plastic cover on top of the faucet's metal handle.
Remove the screw under this cap with an Allen wrench and pull the handle off. Or attach a handle puller to the handle and turn the center knob on the handle puller to pull the handle off for you.
Grip the base of the brass stem, the part under the handle, with a pair of pliers. Turn it counterclockwise to remove it. Take the stem out, which contains the cartridge valve. Unscrew the small screw at the base of the rubber gasket on the bottom with a screwdriver. Pull the gasket off.
Unscrew the nut on the top of the stem by turning it counterclockwise. Pull the rubber O ring off the stem. Place a new gasket on the new stem and tighten the stem screw with a screwdriver.
Insert the new stem into the nut and turn clockwise to thread it. Install the new stem in the faucet and turn it clockwise to tighten. Replace the remaining parts to rebuild the faucet.