The most common reason that a Moen faucet leaks is because the rubber washer in the faucet cartridge has worn out. You can easily replace the washer by turning off the water supply to the faucet and removing the decorative cap. Then remove the cartridge by turning it counter-clockwise.
To avoid a leaky faucet, make sure to test the temperature of your water before using it. Also, pay attention to the way you turn the faucet off. You can fix a leaky faucet by replacing the washers and o-rings on the inside of the handle.