1. **Turn Off Water Supply**: Locate the shut-off valves under the sink and turn them off. If there are no valves, turn off the main water supply.
2. **Plug the Drain**: Use a sink plug or a rag to prevent any small parts from falling down the drain.
3. **Remove Faucet Handle**: Use a screwdriver or Allen wrench to remove the handle. You may need to remove a decorative cap to access the screw.
4. **Take Out the Stem or Cartridge**: Depending on the faucet type, use a wrench to unscrew the packing nut and remove the stem or cartridge. For cartridge faucets, pull it straight out.
5. **Inspect and Replace Parts**: Check washers, O-rings, and seals for wear and damage. Replace any worn parts. For compression faucets, replace the washer and O-ring. For cartridge faucets, replace the cartridge if necessary.
6. **Reassemble the Faucet**: Reinsert the stem or cartridge, tighten the packing nut, and reattach the handle.
7. **Turn On Water Supply**: Slowly turn the water supply back on and check for leaks.
8. **Test the Faucet**: Turn the faucet on and off to ensure it operates smoothly and no leaks are present.
9. **Seek Professional Help**: If the leak persists, consider consulting a plumber.