Unplug the refrigerator from the electrical socket. If you cannot reach the socket, it may be easier to turn off the power at the main circuit breaker. The main circuit breaker could be in the house or the garage. Move the switch that controls the refrigerator to the "off" setting.
Pull the refrigerator away from the wall so you can reach the rear of the appliance.
Use a screwdriver or hex head wrench, as needed, to remove the screws holding the access panel in place on the rear of the Maytag. Set the panel aside. Just behind the panel is the cylindrical compressor, which has hoses snaking out of its sides. The relay connects to the end of the compressor.
Grasp the relay firmly and pull it off the compressor. Depending on the Maytag model, you may need to insert a flat bladed screwdriver in between the relay and the compressor to pry it off.
Loosen the terminals on the old relay with a screwdriver. Pull the wires out of place. Make a note of which wire connects to which terminal. The wires are usually colored white (neutral) and red (hot) or black.
Wrap the wires around the terminal screws of the new relay and screw the terminals in place.
Plug the new terminal in on the side of the compressor. Replace the access panel.
Plug the refrigerator back into the outlet and move it back to the original location.