Shut the water supply off to the sink where the fixture or faucet is attached. If no shut-off valve is installed, turn off the main water supply to the house.
Turn the faucet to its most open position to drain any excess water inside. Then place a towel under the sink to catch any water that may drip onto the floor.
Unfasten the hot and cold water handles by loosening the retaining screws with a screwdriver and/or unfastening the retaining ring or cartridge with a wrench. This will free the faucet from its mounting position on the sink.
Gently twist the faucet stem with a wrench or pry up with a screwdriver. This is where the water pours out when the faucet is turned to the "On" position.
Remove the old gasket from the fixture, it will be a circular piece of rubber or plastic. Take the old gasket to a plumbing supply, hardware or home improvement store. Purchase a gasket of the same thickness and diameter.
Insert the new gasket into the fixture and replace the end of the faucet. Hand tighten it first, then tighten down with a wrench thereafter. Replace the handles in the reverse order of their dissassembly.
Turn the water supply back on and observe the fixture to ensure it does not continue to leak.