Faucets produced by the Moen company are of the cartridge design. At the base of the cartridge is a single rubber O-ring, which is responsible for preventing the faucet from leaking. Given enough time, this rubber O-ring eventually cracks, resulting in leaks. Replacing the existing cartridge with a new one is certainly one way to fix the leaks, but the leaks can also be stopped by simply replacing this O-ring.
Shut off the main water supply at the valve located next to the water meter. The water meter is located outside of the structure, and the valve must be twisted in a counterclockwise direction.
Pry the plastic index cap off of the center of the faucet handle with the blade of a utility knife to expose the screw that holds the handle to the faucet.
Remove the faucet handle by removing the screw in the center of the handle with a Phillips screwdriver, then by lifting the handle away from the faucet valve.
Remove the chrome retaining nut located at the top of the faucet. To remove the retaining nut, grasp the exterior of the nut with an adjustable wrench, then use the wrench to twist the retaining nut in a counterclockwise direction until the retaining nut can be lifted away from the faucet.
Lift the cartridge out of the faucet body, then remove the single rubber O-ring from the bottom of the cartridge. To remove the O-ring, simply pry it off of the cartridge with a flathead screwdriver. Avoid breaking the O-ring, as an exact replacement will be necessary to repair the cartridge.
Lubricate the replacement O-ring with plumber's grease, then slide the O-ring onto the bottom of the cartridge until the O-ring fits securely within the groove at the bottom of the cartridge. Insert the faucet into the faucet assembly, then slide the chrome retaining nut over the faucet. Tighten the retaining nut with an adjustable wrench.
Position the faucet handle onto the faucet, then install the handle's retaining screw with a screwdriver. Press the plastic cap onto the center of the handle to cover the handle's retaining screw. Turn the water supply on at the shut-off valve to complete the repair.