Install a line of cabinet bases in the kitchen island location. These cabinets will serve as both the support and the framework of the island. Use your power drill and wood bit to make pilot holes through the front inside edges of the end cabinet and into the one next to it about halfway up from the floor. Use your screw gun and wood screws to fasten the two cabinets together. Use a countersink bit to recess the screw head so it does not protrude from the inside wall of the cabinet. Repeat the process about 12 inches above and 12 inches below the first screw.
Fasten the back ends of the island cabinet base together. Insert a piece of wooden trim to make up for any spaces between the cabinet bases, and repeat the drilling and fastening processes from step 1. Install a second line of cabinet bases onto the back of the first line and facing in the opposite direction. The idea is to create an island with accessible cabinets on both of its longer sides. If there are gaps between the backs of the two rows of cabinets, use wooden trim to close it up.
Install a finishing panel to the exposed sides of the cabinet bases wherever they are visible. Use your circular saw and a fine-toothed blade to cut the panels to fit. Apply construction adhesive to the rear of each panel where it contacts the cabinet base. Press the panels into position and use your nail gun loaded with small finishing nails to fasten them permanently into position. Install corner trim in the same manner to cover the exposed edges of your panels.
Install a countertop to the cabinet bases. Lay the countertop onto the island frame and use L-shaped corner brackets to mount it in position. Center the countertop on the framework, use your tape measure to check that it is even on all sides, and use your level to check that it is plumb. Install L-shaped corner brackets to the inside of each cabinet base using your screw gun and wood screws to fasten them in place so that the bracket arm is flush with the top edge of the cabinet base and extends outward from the cabinet wall.
Move to the underside of the countertop and use your power drill to make pilot holes into it where the brackets line up. Drive screws into the countertop from below with your screw gun. Install the cabinet doors and drawers all around.