Shut off the gas and electricity at the meter and heating/cooling unit disconnect; most units have an adjacent fuse box with a fuse that you can manually remove to block power. Disconnect gas lines and electrical connections on the unit, with pliers or wrenches. Brace the ducts inside the house which connect to the old unit, so they will not fall down and separate the ducts from the unit. Remove the old unit and set it out of the way.
Set the new unit in place; this may require a forklift or other equipment, depending on the size and weight of the unit. Locate the gas and electrical connections and make sure the supply lines from both utilities will reach without problem. Position the unit with its supply and return plenums facing to the appropriate ducts in the house.
Fasten the unit's vents to a roof vent if the unit is installed inside the house or make sure the unit vents are properly directed outdoors, so no fumes can get into the house. Make sure there is a proper drainage area for condensate water from the air conditioner side; drain it with a PVC pipe to a flower bed or other area where it will run off or evaporate and not create pools.
Connect the gas supply line to the unit's gas intake, usually with a tee connector that has a capped nipple on the bottom, generally secured with screw-type compression fasteners. Make sure there is a cutoff valve between the supply connection and the furnace element. Turn the gas on and test for leaks with a commercial leak detector solution. Spray the detector on the links and look for bubbles; disconnect the supply immediately if there are leaks, indicated by the bubbles.
Make the electrical connections; there should be two, a low-voltage link to the thermostat and a 110-volt line for the unit blower. Connect low voltage lines at the furnace control board; follow a schematic in the unit instruction manual to make the proper hookups, typically involving five thin wires. Connect the line voltage wires to the appropriate terminals on the unit; follow the schematic in the furnace manual, but typically tie black to black, white to white and bare copper to green.
Install the interior ductwork to the supply and return plenums. Slide ducts over the sheet metal plenums, typically a rounded opening, and fasten them with adjustable straps. Seal the seams with heat-resistant tape. Add ductwork if necessary to connect the old ducts with the new plenums, using metal sleeves that fit into the two duct ends.
Restore the electricity by replacing the pulled fuse. Turn the unit on and force it through a heating cycle. Look for any air leaks in the duct connections. Adjust the thermostat to ensure its ties to the unit work properly. Make sure the condensate line drains properly away from the unit.