Map the route of the existing ductwork and identify any changes needed, such as routing new ducts away from unheated spaces. Make sure the openings for existing ducts will accommodate new flex duct and mark any changes on the map. Look for problem areas where flex duct might be bent sharply, and locate replacement routes. Turn off the unit while working.
Remove the old ductwork one section at a time; most ductwork has a large central supply duct, usually down the center of the house, and smaller forks to vents on outside walls. Have replacement ductwork handy. Starting at the farthest vent from the unit, remove the old ductwork by taking it loose from mounting straps or other fasteners, using a pry bar or similar tool.
Place the new ductwork in the pathway and connect it to the vent, but not to a supply duct. Secure it to ceiling joists, wall studs, attic joists or other fastening points used by the old duct. Fasten flex duct mostly with metal mounting straps, which go around the duct and are secured to joists or other permanent fixtures, usually with galvanized nails and a hammer.
Replace one section of ductwork at a time, leaving the central supply and return systems until last. Change the return system, which collects inside air from a central point like a hallway and takes it back to the unit, and alter the filter holder and return entry point if necessary to accommodate an enlarged supply system. Balance return and supply, so the return will collect all the airflow being distributed by the unit.
Connect new flex duct with metal sleeves that go inside the ducts and are fastened with straps on either side. Seal all joints with a heat-resistant tape approved by the duct manufacturer. Wrap the tape completely around the flex duct to cover the seam. Turn the unit on and activate its blower, once all ducts are sealed. Look for any flapping ductwork and listen for any whistling, which indicates air leaks. Repair leaks with tape.