Stand up four 2-by-2-by-36-inch posts on their ends, using an assistant to hold the posts in place in a 16-inch square. Position a 1/2-by-16-by-16-inch board on top of the posts so the posts are in each corner. Drill a hole down through the top board and into each post. Attach the top board to the posts with 3-inch wood screws and consider it the support board.
Set a 1-by-18-by-18-inch board on top of the support board to be the stool seat. Drill four holes up through the support board and into the stool seat. Secure the seat to the support board by screwing 1-inch wood screws up through the support board and into the seat.
Hold two 1-by-2-by-12-inch boards evenly in between each pair of legs in the stool, with these short support boards perpendicular to the posts of the stool. Press the ends of these support boards against the posts and the large surfaces of the short boards facing outward. Drill through each post and into the end of each support board to make two holes in the end of each board. Attach the boards to the posts with 3-inch wood screws.
Position two 1-by-2-by-20-inch boards evenly against one edge of the seat board, with a large side flush against the seat. Make the bottom edge of this board -- which is the backrest support board -- even with the bottom of the seat board, and have the rest of the board extend upward 19 inches above the seat.
Drill two holes into each of these backrest support boards and through into the seat board. Attach the backrest support boards to the seat with 4-inch wood screws in each hole.
Position two 1-by-4-by-18-inch boards evenly across the front of the backrest support boards so that the large side is flush to these boards and they are perpendicular to them. Space the boards evenly on the backrest support boards. Drill two holes through each of these boards, which are the backrests, and into the backrest support boards. Attach the boards with 1½-inch wood screws.