Hire a certified electrician to install an electrical outlet in the cabinet above the range and run the electrical line to the main electrical circuit.
Slide a stud sensor over the wall under the cabinet above the range and mark the location of all studs. Place one end of vent ducting over the inside of the cabinet and verify that it is not positioned in line with one of the studs. Adjust its placement as necessary and draw an outline of the ducting on the cabinet with a pencil.
Drill through the center of the outline with an extension drill bit so it goes all the way through to the exterior of the home. Use a jigsaw to cut out the hole on the inside of the house and then move the fiberglass insulation aside to reach the exterior wall. Draw a similar hole on this wall and cut it out in the same manner as the first.
Fit a vent cap over the hole on the exterior of the home according to the instructions that came with the cap. Caulk around the seam between vent and wall with silicone caulk and allow it to dry.
Tape the paper template that came with the vent hood to the inside base of the cabinet, and center it so it is in approximate line with the range beneath. Push a pencil through the paper at the location of the mounting holes. Also outline the hole locations for the vent tube access and the power cord at this time. Ensure that you make a dark mark on the surface before removing the template.
Drill a 3/8-inch hole through the bottom of the cabinet at one corner of the outlined vent hole. Insert a jigsaw through the hole and cut out the opening for the vent tube to reach the hood. Use a 3/4-inch drill bit to create the hole for the hood's power cord.
Bore 3/16-inch pilot holes down through the indicated marks on the cabinet base. Keep the drill straight so the holes are not angled at all.
Lift the vent tubing up into the cabinet and connect one end to the outside vent using the clips that came with the vent. Apply caulk or spray foam insulation to seal any gaps between the outside vent and the wall hole.
Turn the dial on the top of the range vent so it is set to expel through a vent outside and not simply to recirculation mode. Have an assistant lift the hood so the lip over the vent port fits up inside the cut vent hole. Pull the electrical cord through its hole in the cabinet, but leave it unplugged.
Place the hood's metal retaining plates over the holes inside the cabinet and thread the mounting screws down through the corner holes first. Tighten each of the corner mounting screws with a Phillips screwdriver to hold the weight of the unit before inserting the remaining screws.
Attach the venting to the lip extending from the hood into the cabinet using the clips that came with the hood.
Plug the power cord into the electrical socket in the cabinet and test the operation of the hood fan.