Cut all your lumber to the specified dimensions using your power saw. None of the wood dimensions listed are standard sizes.
Drill two holes through the ends of both 72-inch beams using a drill bit the same diameter as your carriage bolts. Place the holes side by side, 2 3/4 inches from the ends of the beam. Each hole should be 3/8 inch from the nearest side of the beam.
Use the same drill bit you did in step two to drill two holes in one end of each 60-inch post. Place the holes on center, one hole 12 inches from the end and the other 12 3/4 inches from the end.
Sand all surfaces of your lumber until they are smooth and splinter-free.
Set the 72-inch beams and the 36-inch beams together in a rectangular frame, the ends of the 36-inch beams abutting the inside faces of the 72-inch beams. Screw together with two wood screws at each corner. The beams of this frame should lie on their 2-inch sides, with the 4-inch sides facing out.
Lay the 39-by-75 inch plywood sheet on top of the rectangular frame. Screw it in place with one wood screw in each corner, and another screw at the middle of each of the longer sides.
Attach one of the 60-inch posts to one corner of your mattress frame by running carriage bolts through the holes in the frame and the posts. Tighten down the nuts using a crescent wrench.
Repeat step three to attach the remaining three posts to the remaining three corners of the frame.
Set the two 36-inch beams and the two 24-inch beams in a rectangular frame, the ends of the 36-inch beams inside the faces of the 24-inch beams. Like the bed frame, these beams should lie on their 2-inch sides, with the 4-inch sides facing out. Screw them together using two wood screws at each corner, driven through the face of the 24-inch beam and into the end of the 36-inch beam.
Set the smaller plywood sheet on top of the rectangular frame. Screw it in place with one screw in each corner, and one screw at the midline of each long edge.
Place a 30-inch post in one corner of the frame. Screw it in place by driving three screws through the plywood and into the end of the post. Reinforce with one screw each driven through each beam and into the side of the post.
Repeat step three to mount the remaining three posts in the remaining three corners of the desk.