Build a rectangular frame, using all four of your 2-by-4-inch beams. Lay them with the shorter beams on the inside, all beams resting on the narrow edges.
Screw the beams together to connect the frame, using two screws at each corner. Position the screws stacked vertically about 1/2 inch from each other and either end of the beam.
Lay your plywood sheet on top of your frame. Screw it in position with one screw at each corner.
Reinforce the plywood sheet with an extra screw at the center of each short side and two evenly spaced screws along each longer side.
Lay the frame on end, positioned so you can access both sides.
Set one post on end in one corner of your frame, on the side with the beams. Mount it to the plywood sheet with four screws, one in each corner of the beam.
Screw the other three posts into position in the other three corners of your frame.