Move the Maytag MFI2568AES away from the wall and disconnect its power cord.
Turn off the Maytag's water-supply valve. This shutoff is at the back of the refrigerator. The water-supply tube connects directly into this valve. Turn the handle of the valve counterclockwise to shut it off.
Take the ice bin out of the freezer compartment. It is held in place by a few screws that must be removed with a Phillips screwdriver.
Find the wiring harness behind the ice maker. The harness has two locking tabs. Push these together to separate the two halves of the refrigerator's harness. Then pull out the half of the harness that was connected to the ice maker.
Remove the ice maker's mounting screws using a 1/4-inch hex screwdriver. You will find two screws above the ice tray and another just below the ice maker.
Slide the old ice maker completely out of the freezer.
Slide the replacement ice maker into the vacated spot and secure it with the three screws you removed from the old ice maker. Use a hex screwdriver to tighten the screws.
Connect the new ice maker's harness to the harness still within the freezer. Press the two harnesses together until their tabs lock.
Replace the ice bin.
Turn on the water valve on the back of the Maytag, then plug the appliance's power cord back into the wall outlet.