Measure the length of the desk top that will be attached to the wall to make the desk "float."
Mark a level line on the wall that is as long as the desk and at the height you want the desk to be. Between 27 and 30 inches high is typical of most desk heights. Use a stud finder to locate and mark the wall stud points along the line.
Cut a piece of 2-by-2-inch lumber to around 10 inches less than the length of the desk for a wall cleat.
Place the wall cleat on the wall line and secure it to the wall stud points with two 3 5/8-inch screws through the cleat into each stud.
Place an angle bracket flush with the top of the cleat at each of the cleat ends and attach them to the wall through the screw holes in the angle bracket arm.
Place the desk top over the cleat and the horizontal arm of the angle bracket. Secure the desk top to the cleat with screws long enough to go through the cleat and penetrate about 3/4 the thickness of the desk top, from the underside of the cleat into the underside of the desk top so that the desk top surface remains unmarred.
Repeat with the angle bracket arms using screws long enough to penetrate around 3/4 the width of the desk top.