Measure the available cabinet space over your stovetop with a measuring tape to ensure that your hood vent will fit.
Remove the electrical knockout from the hood vent on the side closest to the electrical connection by placing a screwdriver on the knockout tab and tapping the screwdriver handle with a hammer.
Position the hood vent under the cabinet. Using a pencil, mark the positions of the screw slots on the wall and the bottom of the cabinet. Mark the position of the vent on the wall.
Remove the vent hood and cut a vent hole through the wall with a reciprocating saw. The size of the hole depends on the diameter of your vent pipe. Feed a flexible vent pipe through the wall to the outside of the house. Install a vent gasket around the pipe on the outside wall and seal around the gasket with caulk to prevent moisture from damaging your wall.
Drill a 1/2-inch hole through the side and back of the cabinet with a drill to run wiring to the electrical outlet. Shut off the main power supply to your home, remove the outlet cover with a screwdriver and connect the wires to the outlet with wire nuts. Connect the wiring to the motor of the hood fan with wire nuts.
Attach the vent pipe to the vent of the hood. Position the hood in place and attach it to the wall and bottom of the cabinet with wood screws and a screwdriver.
Turn on the main power supply to your home and test the hood's fan and light to ensure everything is working properly.