How do you replace a Moen cartridge 4000?
It seems that Moen has an outstanding customer support, and after emailing them a couple pictures of my faucet to confirm the model they emailed me back instructions to replace the cartridge (along with a confirmation of the cartridge my model was using).

S o basically:


Turn water supply off
Use an allen wrench to remove the faucet's handle
Grab the collar and rotate counter-clockwise. 
Using large pliers or channel locks remove the retainer counter-clock wise
Using pliers grab the white square of the cartridge and remove it from the faucet.


Documentation says that your bare hands should be enough for step #3. This was one of my problems I wasn't sure if I was going to need any tools. It seems that rotating should be enough and force can be applied.

To install the new cartridge you need to pay attention to the cartridge's 3 holes and 2 small tabs protruding. You need to look into the brass chamber to find the location of the 3 big and 2 smaller holes, align the cartridge and insert it making sure you are lining up the three big holes.

Gentle pressure should be able to rotate the cartridge.

After making sure that the cartridge is positioned correctly, you reassemble the faucet.