Transfer the recommended width and length cut-out measurements from the cooktop's installation instructions onto the countertop. Use a tape measure and a pencil to mark the measurements and then use a straight edge and a pencil to connect the marks to make a rectangle.
Standard-sized cooktops measure about 30-inches wide by 21-inches deep. The cutout measurement would subtract approximately 9/16 of an inch from the width and the depth to equal 29 7/16-inches wide by 20 7/16-inches deep. Likewise for smaller 21 1/2-inch wide cooktops, 9/16 of an inch -- or a similar measurement -- is subtracted from the sides of the cooktop to mark the slightly smaller area of its cutout area in the counter.
Drill a hole on the inside of each corner using a large drill bit. Select a bit large enough for the jigsaw's blade or router bit to fit through. Wear goggles for eye protection.
Insert the jigsaw's blade or router fitted with a cutting bit into one of the drilled holes. Cut along the lines, from corner-to-corner, until the center piece falls out.
Check the accuracy of the width and length measurements of the cut-out hole. Use a tape measure to measure across the width sides and then the length sides at the ends and across the middle. Mark any irregular points with a pencil and cut away the excess with the jigsaw.
Sand the inside cut edges of the cut-out in the countertop with a palm sander to make them smooth.
Pass the electrical wire through the top of the countertop's cut-out and then lower the smooth cooktop stove into the hole. The overlap of the sides of the cooktop prevents the unit from falling through the hole.
Screw the support brackets that secure the cooktop to the countertop from underneath the countertop. Align each retainer bracket or spring clip on each side with its screw hole, insert the screw and then tighten with a screwdriver.
Leave the electrical hard-wiring of the cooktop to an electrician, who connects the wires to the power supply in the junction box for the cooktop and makes sure the unit's power supply and hook up meets local building code standards.