A noisy washer-type faucet is usually caused by a loose seat washer. To stop the noise, first turn off the water and take the faucet apart as described previously. If the washer is loose, tighten it or replace it. After threading the stem back into the faucet body, try moving it up and down. If it moves, the stem is worn and the entire faucet must be replaced.
Some faucets are noisy due to poor design and construction.
The only way to solve this problem is to replace the faucet with a quality one. Then take the faucet apart by removing its handle, escutcheon and packing nut. The packing nut may be buried deeply in the wall, requiring a socket wrench for removal. Your bath and shower faucets may have a renewable seat that can be smoothed with a seat-dressing tool or removed and replaced using a seat wrench. For replacing and repacking the washer, follow the same instructions provided for a washer-type faucet.