Hold the vent on the door at the location where you'll install it. Lay a level on the vent's top edge to make sure it is straight. Trace a pair of horizontal lines on the door using the vent’s top and bottom edges.
Measure the width of the door, and divide the measurement by 2. Place marks at the centers of the traced horizontal lines at this measurement.
Measure the width of the vent, and divide the measurement by 2. Place marks at the centers of the vent's top and bottom edges at this measurement.
Remove the hinge pins that secure the door to the jamb. Place the door, traced lines face-up, onto a pair of sawhorses.
Place the vent on top of the door, and line up its edges with the traced horizontal lines. Slide the vent so that its top and bottom center lines match the lines on the door. Trace around the base of the vent with a pencil.
Equip an electric drill with a 1/2-inch drill bit. Drill a hole into the door, anywhere within the traced lines, to create a starting point for the jigsaw blade.
Equip the jigsaw with the correct cutting blade. Slip the blade through the drilled hole in the door. Turn on the jigsaw, and follow the traced lines to cut out the space for the vent.
Insert the base of the vent into the hole. Secure the vent to the door with fasteners and a screw gun. Flip the door over to expose the hole on the opposite side, and attach the back of the vent. Secure the second half of the vent with fasteners. Rehang the door.