Shut off the main water valve to cut off water to the faucet. Alternatively, turn off the valve on the line that supplies water to the bathroom. Release water pressure on the faucet before disassembling it by opening the faucet.
Find the screw that holds the handle as a starting point to disassembling the faucet. The screw can be behind or under the faucet lever. Some screws are covered by a cap. Look for a groove at the front side of the faucet, and use a flat-head screwdriver to pry off the cap. Uncover the valve to find the cartridge.
Use the needle-nose pliers to pull out the retaining pin. Consider the orientation of the cartridge before removing it to avoid confusion when putting it back. Some cartridges are held in position by a collar.
Wrap a rag around the collar to prevent damage to the finish before unscrewing the collar using adjustable pliers. Consider a special tool for extracting the cartridge if it has been a long since the faucet was last serviced. Extract the cartridge to clean, or replace worn out washers and O-rings. If the cartridge is worn out, replace it. If it is full of mineral deposit, dissolve the mineral deposits by soaking the cartridge in white vinegar.