Stop a dripping compression faucet by shutting off the water and replacing the worn washer or O-ring.
Turn the shutoff valves under the sink clockwise until they stop, then open the faucet to release pressure. Place a rag or stopper in the drain so small parts can't fall in.
Pry off the decorative cap on top of the handle with a flat screwdriver, remove the screw underneath, and lift the handle off. Spray penetrating oil if it's stuck.
Use an adjustable wrench to loosen the packing nut, then pull out the valve stem. Note the order of parts as you go so you can reassemble correctly.
At the bottom of the stem, remove the screw holding the worn washer, fit an exact-match replacement, and swap the O-ring around the stem. Take the old parts to the hardware store to match the size.
Put the stem, packing nut, handle, screw, and cap back in reverse order, turn the water back on slowly, and run the faucet to confirm the drip is gone.