Turn off the electrical supply to the AC unit where the contactor is mounted. This can be done either at the main circuit breaker or at a subpanel mounted outside by the condensor unit. Shut off both the breaker for the inside and outside unit on a split system.
Locate the service panel on the condensor unit outside. This is usually on the side of the unit. There may be an electrical warning sticker on the outside to help you identify it. Remove the cover with a screwdriver.
Locate the connector, which is a small, electrical panel mounted in the access space. You should be able to see the connector plates on the interior of the fixture, and there will be a number of different colored wires connected to it.
Make a note of which colored wire is connected to which terminal on the contactor. Use a pen and paper to make notes or take a picture with a digital camera.
Use a screwdriver to loosen the terminals. Pull off the wires with a pair of needle-nose pliers if necessary. Loosen the larger screws or bolts that hold the contactor in place on the AC unit. Pull the contactor out of the condensor. .
Insert the new contactor into the AC unit and secure it in place with the mounting screws or bolts. Replace the wires on the correct terminals according to your notes or photos.
Replace the access panel then restore power to the AC unit. Turn the thermostat down so that the AC unit starts to check your work.