Use a screwdriver to remove the screw holding the handle cap in place, if your Moen faucet has one. If not, use a flat head screwdriver to pry the handle cover away from the faucet.
Unscrew the exposed handle screw with a 7/64 inch hex wrench. Use a pair of pliers to unscrew the handle retainer nut and pull it up.
Pull the entire spout up while rotating it sideways until it comes away from the sink. Pull the old o-rings off the valve body.
Mix 1/2 cup vinegar and 1/2 cup water in a bowl. Dip a clean sponge in the solution and gently scrub the inside of the faucet. Wipe down the outside of the valve.
Coat the new o-rings in silicone grease and lower them in place over the valve body. Coat the outside of the valve and the inside of the spout with the silicone grease, then lower the faucet back into place.
Reattach the retaining nut with the pliers and replace the handle.