Have an assistant hold up four 1-by-1-by-36-inch posts and place a 1/2-by-12-by-12-inch wood block on top of them. Maneuver the four posts into the absolute corners of the wood block and drill a hole down through the top of the block and into each post. Secure each post to the block with a 2-inch wood screw tightened completely into the hole.
Position a 1/2-by-2-by-10-inch block between each set of posts, with the largest surface facing out and the long, thin surface against the underside of the top block. Drill down through the top block into this board, which is a side board. Make three holes in the top block and each side board for a total of 12 holes. Set 2-inch wood screws in each hole and tighten the side boards securely to the top block.
Position two additional 1/2-by-2-by-10-inch blocks between two opposing sets of posts, 2 feet up from the ground. Drill two holes through each side post and into each end of both blocks, for a total of eight holes. Set a 2-inch wood screw in each hole and screw them tight to fasten the boards in place. Repeat this process for two more 1/2-by-2-by-10-inch boards, perpendicular to these and 1 foot off the ground.
Place a 1-inch-thick board with a 16-inch diameter upside down on the working surface. Set the top block of the stool assembly upside down against the underside of this thick board, which is the bar stool seat. Drill four holes down through the top block and into the seat, being careful not to puncture the seat surface. Drill 2-inch screws into each hole to fasten the seat to the rest of the stool. Stand the stool upright and sand the seat if necessary.