There are two styles of Moen faucet. With the older faucet, the entire handle is pulled out and pushed in toward the base to control the water flow. With the newer style, only part of the handle is lifted to turn the water on and off. The newer style has more parts, so disassembling the faucet will be more time-consuming.
Locate the setscrew in the handle. The screw may be in the front of your faucet handle. If it is not, it is located underneath the cap on top of the handle.
Pry off the cap on top of the handle with a screwdriver to expose the screw, if necessary.
Unscrew the set screw in the handle.
Lift off the handle, exposing a round stainless cartridge collar with an indent that points up.
Remove this cartridge collar by pulling up on it manually. This will expose the top of a cylindrical cartridge being held in place by a U-clip.
Grab the top of the U-clip with needle-nose pliers and pull it straight up and out.
Grab the top of the cartridge with the pliers and pull it out. If the cartridge is stuck, pull harder and it will come out.