Shutoff your main water supply and bleed the water lines running to the bathtub. Your water main will be in the lowest point of the house and have a shutoff valve attached. Turn the shutoff valve clockwise until it is closed, then turn the faucet on in your bathtub. When water stops running from the tub faucet, turn it off. Drape an old towel underneath the tub spout to protect the tub in case anything falls while working.
Inspect your tub spout. If there is a screw on the underside of the tub spout, use a Philips-head screwdriver to remove it. Once the screw is out, wrap your hand around the spout and turn counterclockwise to remove it. If your tub spout has no screw, simply rotate the tub spout counterclockwise by hand to remove it.
Disconnect the faucet knob. Depending on your model of Moen tub faucet, the handle will have a plastic disc with Moen's logo or visual directions for hot and cold water. Use the flat-head screwdriver to pop this disc off the faucet handle and reveal the setscrew. Loosen and remove the setscrew with the Philips-head screwdriver.
Slide the faucet knob off the handle to reveal the fixture's stem and collar. Grasp the collar with your hand and loosen it by turning it counterclockwise. Using an adjustable wrench, twist the interior plumbing stem counterclockwise until disconnected and remove by hand.
Remove the Moen fixture by loosening the hot and cold water supply lines. You should be able to fit an adjustable wrench into the opening in the wall and loosen the hot and cold water supplies, as well as the feed line for the shower head. Gently remove the Moen fixture from the wall.
Apply a new coating of Teflon tape to the threads of the supply lines and shower feed line. Connect these lines by hand, one by one, to the Pegasus tub fixture and tighten with a wrench.
Connect the Pegasus tub spout to the exposed pipe. Slide the new spout over the pipe until the threads meet, then turn clockwise until tight.
Slide the face plate, or escutcheon, over the pipe stem and screw into place, then slide the stem sleeve on top. Secure the handle seat to the stem with the setscrew.