Check the airflow output of the unit, which is located on a plate on the unit or in an owner's manual, to make sure it is adequate to handle an addition. Adding a duct to a unit that already is at capacity simply will reduce airflow to existing outlets, so you may wind up with two cool rooms. This can be a complex calculation, involving the size of the unit, size and length of existing ducts, and size and length of the planned addition.
Locate the spot for the new vent or vents for the added duct work, as well as the place on the existing duct work where it should attach. Find the most direct route between those points and check it for any hot water pipes, other heat sources, electrical boxes or other impediments to installation. Plan for a return duct to collect air from the new space and return it to an existing return duct or run a new return duct.
Cut into the existing duct with tin snips. Flex duct is formed with coiled wires surrounded by fiberglass insulation and covered with a metallic barrier. Open the duct enough to slide in a sheet metal T connector, with two ends that go into the existing duct and a T for the new duct. Secure the old duct to the connector with adjustable straps and seal the connection with heat-resistant tape.
Slip the new duct work over the T, securing it with adjustable connectors and tape. Run it to the new outlet, between ceiling joists if possible, or across them if necessary. Support the new duct about every 6 feet with metal straps 1 1/2 inches wide that go under the duct, and are nailed to wooden joists on both sides with galvanized nails and a hammer.
Install a new return duct with the same capacity as the new supply duct. Duct work must be balanced so a return system collects all the air that is pushed out by the unit. Fasten return ducts with adjustable straps and tape, just like supply ducts. Return ducts must connect behind an air filter installed at the return entry point or points in the house.