You should also shut off the water supply from the sink

You should also shut off the water supply from the sink handles to the knobs underneath which controls the entry of water.
https://www.batten-machinery.com/product/imm-screw-barrel/
If an O-ring is damaged, cut it off using a utility knife. Then, place a new O-ring using a flat-head screwdriver to guide you. Remove the Handles. Expose the screw holding the handle. They all screw barrel have a central, swivelling arm which you can adjust from hot to cold. Unscrew it and gently remove the handle. Remove the handle knob’s decorative parts with a flat-head screwdriver. Avoid making a bigger problem by transforming your faulty faucet into screw and barrel for extruder a fountain. Do this using your hand.

3. Find out what type of faucet you’re dealing with. Check both the hot and cold water handles to make sure they’re both working properly without leaks. Replace the seats with new ones. Inspect for damage. This will expose the screw that attaches the handle to the faucet’s stern. This will prevent screws or washers from going down the drain. Inspect the rubber washer.

. You will need flat-head screwdriver and/or Philips, adjustable wrench or a C wrench, slip-joint pliers, replacement washers and O-rings, sink plug, and penetrating oil such as CRC or WD-40. Plug the drain with a sink plug or a rag. A compression type faucet consists of two screw handles for hot and cold water.

6.

1. Here’s a step-by-step guide to stop a faucet leak.

8.

4. If the washer is damaged, then remove the screw and have it replaced with a new one.

5. If the valve seat has damage, get a seat wrench to get rid of the damaged seats. Reassemble the faucet. Turn off your main water supply. Then, coat a new one using heat proof grease. If it looks fine, then remove the packing nut and see if the O-rings are damaged. Turn the water supply on. Check the stern assembly for any signs of damage.

9. The other three types share something in common. Look for rough spots.

Whether you’re having a pool under your sink, or you’re starting to get annoyed to the creepy dripping sound that keeps you up all night, a simple faucet leak can easily turn into a bigger problem if not fixed properly. There are four common types of household faucets - compression faucet, ball faucet, cartridge faucet, and ceramic-disc faucet. If your compression-type faucet keeps on dripping after the handles are shut off, remove both handles and check the stern assemblies for any signs of damage. You may have to disassemble your faucet to know what type of faucet you’re dealing with.

7. If the O-rings and washer are fine, check around the valve seat for any rough spots. Use slip-joint pliers to loosen the retaining nut which mounts the stern in place. Then turn the faucet on back again to drain any remaining water. However, the three types vary in the internal mechanisms working underneath their arms. It’s a good thing that repairing a leaky faucet can be quite simple and inexpensive. When you’ve finally detected the problem and fixed it, the next thing to do is reassemble the faucet