Find the location of any nails or screws on the floor surrounding the vent -- these will indicate the location of the nearest floor joists. Draw a rectangular box around the existing vent that encompasses the nearest joists on each side and provides 2 to 3 inches of clearance around the existing vent on the other two sides of the rectangle.
Remove the screws securing the existing vent to the floor and take the vent out.
Cut out the sketched rectangular opening from the floor starting from the space provided by the vent opening. Vacuum out any sawdust or debris from the venting with a shop vac.
Measure the thickness of the flooring with a ruler. Place the new vent onto a piece of medium-density fiberboard, or MDF, that's the same thickness and trace the opening size onto the sheet. Cut out the vent opening in the MDF.
Trace the floor opening onto the MDF and cut out the replacement piece. Place the new flooring piece onto the floor and screw it into the floor joists with wood screws. Place the new vent into the floor and attach it with the supplied screws.