Turn off the water supply: Locate the shut-off valve under the sink and turn it off to cut off the water supply to the faucet.
Disassemble the faucet: Use a wrench or pliers to loosen the nuts and screws that hold the faucet in place. Take the faucet apart carefully and lay out the pieces on a towel in the order you remove them.
Inspect the parts: Check the rubber washers, O-rings, and other small parts for wear and tear. If you notice any signs of damage or decay, these parts need to be replaced.
Replace worn parts: Take the worn parts to a hardware store or plumbing supply store to get the correct replacements. Be sure to match the size and shape of the parts to ensure they fit properly.
Reassemble the faucet: Reassemble the faucet in the reverse order of disassembly. Tighten the nuts and screws carefully, and ensure that all parts are in their correct position.
Turn on the water supply: Turn on the water supply and test the faucet to see if the dripping has stopped.
If the dripping continues even after you've replaced the worn parts, there may be a more serious problem with the faucet that requires the help of a professional plumber.