Turn your breaker panel off by turning off the main breaker located at the top of the electrical panel. Remove the cover from the breaker panel using a Phillips or slotted screwdriver.
Test to confirm proper disconnection of power by touching one probe of a two probe electrical tester to a screw on any breaker. Touch the remaining probe to any metal on the breaker panel. The tester should fail to light or register any wattage with proper power disconnection.
Pull the 10/3 nonmetallic (NM) cable from the air-conditioning unit to the electrical panel. Use a wire cutter/stripper to remove the exterior sheath from the NM cable, exposing the red, black, white and bare copper wire. Strip 3/4-inch of insulation off each wire.
Install the 40-amp double pole breaker into the breaker panel by sliding the back of the breaker into the breaker slot and push the front of the breaker on to the center buss bar.
Slide the red wire under one screw at the rear the 40-amp double pole breaker. Slide the black wire under the remaining screw on the breaker and tighten both screws.
Attach the white wire from the cable to the neutral bar by sliding it under a set screw on the bar. The neutral bar is the silver bar located inside the breaker panel and all white wires connect to it.
Attach the green wire from the cable to the ground bar by sliding it under a set screw on the bar. The ground bar is similar to the neutral bar but all the bare copper and green wires attach to it.
Replace the cover on the main breaker panel and turn the main breaker back on.