A Moen faucet repair is a cartridge faucet. These cartridges change from model year to model year. Even though they still use the same replacement cartridge, older units have different pivot mechanisms than the new ones. If you get the replacement cartridge, it comes with instructions and pictures that will guide you through the replacement.
Typically what has to be done is the top cap where the handle attaches to the faucet is removed to expose a Phillips screw. Once the screw is removed, the metal handle and plastic guide assembly will slip off. You will see a brass stem that the screw went into and a clip that retains it. Delta faucet repair
On most models, a cone or shroud prevents you from getting to the clip, if they unscrew you will be able to remove the clip. Be sure to turn off the water before removing the clip. Usually you can grab the stem with pliers and pull the cartridge out. When the cartridge is frozen and it will not pull out, you will want to use a tool to rotate the cartridge and loosen it up.
Most replacement cartridges come with a plastic tool made just for this job. Occasionally the plastic tool is not enough and you will need to rent a cartridge puller to remove it.
Once it is out, the job is all downhill. Insert the new cartridge, slide in the clip, replace the cone, and turn on the water.
Why turn on the water before the handle is attached? Because if hot and cold are reversed all you have to do is rotate the stem 180-degrees and you are good to go. Just so you know. And the clip is not removed when you do this.