Determine where the ducting is going to run. The updated plans for the house will be very helpful in doing this. The most important factor in this decision will be if the house has a cellar or crawlspace, an attic or crawlspace, or both. If the house has both, you have to decide between the ceilings or the floors -- or both -- for the vent openings. Cut vent openings in floor or ceiling and install metal duct openings. If the openings are in the ceiling, use the drywall saw, if it's the floor, use the wood saw. Cut an appropriate opening for the air inlet that feeds that air handler/heat exchanger. Install appropriate sized ducting between this opening and the inlet for the air handler/heat exchanger.
Determine where the furnace and air handler will go and mount them per manufacturer instructions. Route the ducting from the furnace to the farthest opening. Install a Y-pipe for each duct opening. Adding a second Y-pipe will allow for two openings in rooms close to each other. Install hard ducting to within 3 feet of the duct opening and connect with flexible ducting. Repeat this for every duct opening. If necessary, cap the main duct with a duct cap.
Secure all of the ducting connections by installing 3 self-tapping screws evenly spaced around each connection. Liberally coat each connection and screw location with sealing putty. Use the drill with a Phillips screwdriver tip to install the self-tapping screws.
Route the 20-gauge twisted pair from the furnace unit to the location you desire to mount the thermostat per the instructions that come with it. Connect the wires at either end according to installation instructions for each unit. Connections to the thermostat will require a Phillips screwdriver while furnace-side connections may be two wires that need to be twisted together and secured with wire nuts or a screw block like the thermostat.
Route the 12-2 ROMEX® from the furnace and air handler to the electrical fuse/breaker panel. Connect black to black and white to white. Securely twist wire nuts clockwise onto the two connections. Connect the bare wire to a secure ground.
Turn off the main power to the panel. Loosen the clamp on one of the groups of wires entering the electrical panel. Remove the dead front panel, if so equipped, usually by turning 4 to 6 screws counterclockwise with a screwdriver (either type). Pull enough of the ROMEX® into the panel to reach the ground bar with enough slack to route around the edges of the panel. Strip the outer cover from the 3 conductors. Connect the bare wire to the ground bar turn the screw clockwise with a small straight screwdriver to tighten it. Strip ¼ inch of the white wire using the wire strippers and insert it into the bar with the other white wires. Tighten the screw using a small straight screwdriver. Tighten the screws on the wire clamp.
Add up the values of the breakers/fuses in the box, separating the sum into left and right sums. Most likely you will have to move breakers or fuses to balance the load. Strip ¼ inch of the black wire and insert the end into the breaker. Tighten the screw to secure the wire. Install the breaker so as to ensure proper load balancing. Reinstall the dead front panel. Turn the main power back on and test the central heating once the gas is hooked up. Secure the ducting to the frame of the house in several locations using the strapping and the self-tapping screws.