Position the vent hood above the island on the ceiling. Mark the outline of the vent hole on the ceiling. Also, mark the position of the electrical cord that powers the vent fan.
Cut through the drywall along the vent hole outline with a keyhole saw. Cut a 1-inch hole for the electrical cord.
Trace the outline of one end of a flexible vent pipe on the exterior of the home above the ceiling drywall. Cut along the outline through both sides of the wall with a reciprocating saw.
Feed a flexible vent pipe through the ceiling hole and along the ceiling joist to the hole in the exterior wall. Fit an aluminum flashing ring over the end of the vent pipe. Apply caulk around the end of the pipe and between the flashing ring and the siding.
Feed the power cord through the 1-inch ceiling hole to the nearest electrical outlet. Turn off the main power supply to your home. Remove the outlet cover with a screwdriver. Connect the black power cord wire to the black electrical outlet wires with wire nuts, and wrap electrical tape around any additional exposed wire. Connect the white power cord wire to the white electrical outlet wire in the same manner. Do not turn the main power supply back on until you have replaced the outlet cover. Exercise extreme caution when working with electrical wires; if in doubt at any point, consult or hire an experienced electrician.
Connect the end of the vent pipe to the vent hole in the hood. Using an electric screwdriver, attach the hood to the ceiling with 2-inch wood screws.