Replace Washer or O-Ring
The most common fix for a dripping faucet, especially compression and cartridge types. A worn washer or O-ring no longer forms a watertight seal, allowing water to seep through even when the handle is fully closed.
Steps
Turn off the water supply valves under the sink and open the faucet to relieve pressure. Remove the handle by unscrewing the decorative cap and handle screw. Pull off the handle and unscrew the packing nut to expose the stem. Remove the stem and locate the washer (at the bottom, held by a brass screw) or O-ring (around the stem body).
Finding the Right Part
Take the old washer or O-ring to a hardware store to match the exact size and type. Compression faucets use flat or beveled seat washers, while cartridge faucets use O-rings specific to the cartridge model.
Reassembly
Seat the new washer or O-ring, coat it lightly with plumber's grease, reassemble the stem and handle, and turn the water supply back on. Check for leaks at both the spout and handle base.