Moen makes several types of double handle bathroom faucets. Each one features a handle to adjust and control the hot water and a handle to control the cold water. In each handle is a small cartridge valve in a sealed cylinder. This is the part to replace when leaks form or your faucet is not producing the proper temperature water. It's a fix anyone can complete in as little as 10 minutes, provided you have everything ready.
Close the water valves to the faucet. There are two under the sink. Turn each one clockwise until they stop to close them completely.
Take the plastic plug cap off the top of the Moen faucet handle and unscrew the handle screw under it with an Allen wrench, then slide the screw out of the handle. Pull up on the faucet handle to remove it from the cartridge.
Unscrew the cartridge nut with a pair of pliers or hex wrench. This nut is right under the handle. It holds the cartridge in place within the faucet's handle base.
Take out the cartridge and replace it with another Moen bathroom faucet cartridge, one designed for the model faucet you own. Slide it into the faucet handle base and replace and tighten the cartridge nut. Install the handle and tighten the small screw on top of the handle.
Repeat the process on the other side of the faucet to repair the leak or poor temperature performance, if necessary. Only perform these steps on the handle that has the problem.