Set two 37-inch boards on edge, parallel, and space them 23 inches apart. Set two 23-inch boards between them at right angles and space them 35 inches apart so their sides are flush with the ends of the 37-inch boards. Screw through the 37-inch boards and into the ends of the 23-inch boards using eight screws. This frame is the top frame to your shoe bench. Repeat this step two more times to build the frames for the lower shelves.
Stack the three frames so the sides of the frames are parallel. Position a 26-inch board perpendicularly inside each corner. Screw through the bottom frame and into each 26-inch board using two screws for each board. Lift the middle frame 6 inches above the lower frame and screw it to the 26-inch boards using another eight screws. Lift the top frame 8 inches above the middle and screw it down using another eight screws. This is the shoe bench frame and it is upside-down.
Turn the shoe bench frame upright and lay the 37-inch plywood on top of the frame so the edges are flush. Screw the plywood to the top frame using 16 screws, four screws for each board. Set the 31-inch plywood sheets on the lower shelf frames, one on each frame so the edges are flush. Screw the plywood sheets to the frames using eight screws for each sheet.