Locate the placement for the desk. Determine exactly where you want the desk mounted within the space.
Cut the 18-inch by 24-inch sections to form two triangles. Create a line from one corner to the opposite bottom corner, forming two 18-inch by 24-inch triangle sections. Cut the rectangle into these two sections.
Attach mounting wood to triangles. Select one cut triangle, one 2-inch by 18-inch section, and one 1-inch by 24-inch section. Apply wood glue around the 18-inch edge of the triangle, and center the 2-inch by 18-inch section along this edge. Place nails at each corner and one in the center. Repeat this process for the 24-inch edge of the triangle and the 1-inch by 24-inch section. Continue this process with the remaining 24-inch by 1-inch section, 2-inch by 18-inch section, and the 18-inch by 24-inch triangle.
Attach mounting triangles to the top of the desk. Place the top of the desk on a flat surface with the bottom side facing up. Measure in 6 inches from each end. Apply wood glue to the 24-inch side mount of the triangle, and place one triangle on each 6-inch mark so the triangle extends from the front to back edge of the desk, with the 18-inch edges facing the back of the desk. Use small nails lined along the 1-inch by 24-inch placed on both outer edges 4 inches apart.
Mount the desk to the wall. Press the 2-inch by 18-inch sections firmly to the wall. Verify that the desk is level, and nail the mounts into the wall. Place nails along both edges of the mounts for each triangular section. Apply nails every 4 inches from top to bottom of mounts on both sides.