Before starting any work, ensure you have all the necessary tools and your new replacement cartridge. Lay out your tools on a towel next to the sink to keep them organized and prevent scratching your countertop. Having everything ready will make the process smoother and quicker.

Look inside the cabinet directly under your kitchen sink. You will find two small valves, one for the hot water line and one for the cold. Grasp the handle of each valve and turn it clockwise (righty-tighty) until it stops. This will shut off the water flow to the faucet. To confirm the water is off and to relieve any pressure in the lines, lift the faucet handle to the 'on' position. A small amount of water may trickle out, but it should stop completely within a few seconds. Leave the faucet handle in the open position to allow it to drain fully.

Place a thick towel or a rag over the sink drain. This is a critical step to prevent any small, crucial parts like set screws from accidentally falling down the drain. The towel also serves to protect the sink's surface from being scratched by tools.

Locate the small decorative cap on the faucet handle, often marked with a red/blue hot/cold symbol. Carefully use the tip of a flathead screwdriver or a utility knife to pry this cap off. Underneath, you will find a small set screw. Select the correct size Allen wrench from your set and insert it into the screw. Turn the Allen wrench counter-clockwise to loosen the screw. You only need to loosen it a few turns; you do not need to remove it completely. Once loose, lift the entire handle straight up and off the faucet body.

With the handle removed, you will see a rounded or dome-shaped metal piece called the dome cap. This part is usually threaded. Grasp it firmly and turn it counter-clockwise by hand to unscrew it. If it's too tight, wrap a rag around it and use adjustable pliers to get a better grip and turn it loose. Lift it off to expose the plastic components and the cartridge retaining clip.

Look at the top of the brass faucet valve body. You will see a small, U-shaped metal clip inserted into two slots, holding the cartridge in place. Using needle-nose pliers or the tip of a flathead screwdriver, firmly pull this clip straight up and out of the faucet body. Be careful not to bend or damage it, as you will need to reuse it.

The old cartridge is now free to be removed. Many Moen replacement cartridges come with a small plastic tool designed to help with this. Insert the tool over the cartridge stem and use it to rotate the cartridge back and forth to break the seal. Then, grasp the stem of the cartridge with adjustable pliers and pull it straight up and out of the faucet body. This may require some wiggling and steady force, especially if there is significant mineral buildup.

Before inserting the new cartridge, inspect the inside of the faucet's valve body. Use a rag or a soft brush to wipe away any mineral deposits, sediment, or rubber debris left from the old cartridge. Ensuring the interior is clean will allow the new cartridge to seat properly and create a perfect seal.

Take the new cartridge. If you have plumber's grease, apply a light coat to the rubber O-rings to help it slide in easily and prevent tearing the seals. Align the cartridge correctly; there are typically tabs or notches on the side of the cartridge that must fit into corresponding slots inside the faucet body. For a Moen 1225 cartridge, the 'H C' marking should be facing up. Push the cartridge firmly and evenly down into the valve body until it is fully seated.

Reassemble the faucet by following the disassembly steps in reverse. First, re-insert the U-shaped retaining clip into its slots to lock the new cartridge in place. Second, screw the dome cap back on, hand-tightening it until it's snug. Third, place the handle back onto the cartridge stem, ensuring it is oriented correctly. Finally, use the Allen wrench to tighten the set screw (clockwise) and then gently press the decorative cap back into its place on the handle.

With the faucet fully reassembled and the handle in the 'off' position, slowly turn the hot and cold water shut-off valves under the sink counter-clockwise to restore the water supply. Open them fully. Now, check for leaks around the base of the faucet handle and from the spout. Turn the faucet handle on, moving it from hot to cold to test its function and flush out any air in the lines. If there are no drips from the spout when it's off and no leaks around the handle, the repair is complete.