Turn off the power for the kitchen circuit at the breaker box. Measure the countertop on the island using a tape measure and mark the dimensions you need to cut with a pencil. Drill a starter hole in the countertop using a drill and a drill bit large enough to allow insertion of the jigsaw blade.
Insert the blade of the jigsaw into the starter hole and cut away at the countertop to accept the stove unit. Check to be sure that the countertop is level. Use wooden shims between the countertop and the base cabinet to make it level if it is not. Insert the stove into the opening in the countertop. Secure it in place with the locking clips at the bottom of the appliance. Access the locking clips from inside the cabinet base.
Connect the electrical wires to the stove. Red or black wires are hot and white or gray are neutral. Connect the wires according to color and install wire nuts over the splices. Connect the ground wire to the stove unit. It will be a green wire or a bare wire. Tighten the screw using a Phillips screwdriver.
Seal the edges of the stove where it meets the countertop using a caulking gun with a tube of caulk in it. Connect the vent to the exhaust on the stove unit and tighten the clamp using a Phillips screwdriver. Turn the circuit breaker on for the kitchen power supply.