Inspect the area where you want to place the vent to ensure that you will not need to move wiring, cables or other obstructions. Shut off the power supply to the furnace.
Remove the existing floor vent from the floor. Measure the width and length of the bottom of the vent with a measuring tape to determine the size of the hole you need to cut in the floor for the new vent location. Check to ensure that the new vent location does not cross a floor joist. Mark these measurements on the floor, using a ruler as a guide, to create an outline of the cut.
Drill a 3/8-inch hole at one corner of the outline with a hand drill. Insert the blade of a reciprocating saw into the hole and cut the floor along the outline. Insert the vent into the hole so that the lip of the vent supports the vent on the floor.
Cut a straight line along the duct with tin snips near the old vent location. Unscrew the top of the duct from the underside of the floor with an electric screwdriver. Place the top section of the duct in the new location and reinstall it by driving galvanized screws through the holes into the underside of the floor.
Measure the gap between the duct sections. Cut a new duct section to fit this length with tin snips. Place a duct collar on each end of the new section and fit it in the gap to connect the vent in its new location.
Drill through the holes in the duct collars into the duct sections. Insert and tighten galvanized screws through the holes to secure the sections.
Turn on the furnace power supply and check to ensure that air flows through the duct and vent correctly.