Cut out the table components from a sheet of finish grade 3/4-inch plywood. These should include a top and bottom desk plate measuring 20-by-50 inches, two side plates measuring 20-by-6 inches and a back mounting plate measuring 6-by-48-1/2 inches.
Place the two side plates on the floor, standing on their long edges parallel to each other, with the back mounting plate placed on its long edge between the ends of the two side plates. Place the desk top section (20-by-50 inches) on top of of these side and back sections so that the edges of the top plate sit flush to the side and back plates.
Screw a wood screw through the top plate into the edges of the side and bottom plates every 4 inches along each of the three sides of the top plate.
Turn the screwed-together top, side and back plates over and place the bottom plate over it flush along the edges, and screw it down to the desk assembly through the bottom plate into the edges of the side and back plates. You should now have a five-sided box.
Use a stud finder to locate the studs in the wall where you wish to install the floating desk. Studs in walls are generally spaced every 12 to 18 inches from each other and are made of spruce or other woods in 2-by-4 or 2-by-6 vertically oriented planks. Locate the center of each stud to ensure the solid mounting of your desk.
Mark the location of each stud on the wall with the help of a spirit level to ensure that the marked holes are level. Mark the location of the studs at the height you would like to install the desk. Mark the spacing and location on the back of the back plate of your desk along the center line of it.
Drill pilot holes into the wall and studs where marked using a 1/4-inch drill bit, then drill out the corresponding holes into the back plate of the desk using a 1/2-inch drill bit.
Hold the desk up to the wall with the help of a friend and match up the holes in the back plate with the pilot holes drilled into the wall. Insert lag bolts through the holes in the back plate and screw them into the studs in the wall. Ensure that all bolts are firmly torqued into the studs with a socket wrench. This will firmly mount the desk assembly to the wall, also creating a shelf in between the desk's top and bottom plates, providing a small storage area to allow you to keep the desk surface tidy.