Cut the plywood sheet along the diagonal, creating two right triangles. Keep one. Discard the other or use it for another project.
Sand all faces of your lumber using coarse grit sandpaper. Sand a second time with fine grit paper. If you want to paint or stain the desk, do so at this point.
Set one 32-inch long post on end at the right angled corner of the plywood, its outer edges flush with the edges of the triangle. Attach it using one wood screw, driven through the plywood and into the end of the post.
Lay a 36-inch long post along one edge of the plywood, its end abutting the one face of the 32-inch post. Attach it with three evenly spaced wood screws driven through the plywood and into the face of the beam beneath.
Repeat step four to attach the other 36-inch post along the other flat side of the triangle.
Set a second 32-inch post on end at the opposite end of one 36-inch post. Its outside edge should be flush with the edge of the triangle and one face should abut the end of the 36-inch post. Connect it with one wood screw driven through the plywood into the end of the post.
Repeat step six to mount the remaining 32-inch post on the end of the remaining 36-inch post.
Reinforce the posts by driving a screw through the face of a 32-inch post and into the end of the 36-inch post. Do this for each of the four points where the posts connect.
Add a second coat of paint or stain if you're painting the desk, covering the screw heads as you do so.