Measure the corner where you want to install the desk and mark a line on each wall at the height you want the desk, and the length the corner desk will come out from the corner.
Locate the wall studs using a stud finder and mark them in on the level line.
Cut two pieces of 2-by-2 lumber to around 4 inches less than the length of the desk sides for the cleats. Position each cleat on the wall lines, around 2 inches in from the end of the lines.
Secure the cleats to the wall with two 4-inch drywall screws driven through each of the wall stud points.
Cut a triangular piece of 1-inch-thick MDF to the dimensions of the corner desk. Place the desktop over the cleats and push it flush into the corner.
Secure the desktop to the cleats using 2-inch wood screws driven through the desktop into the cleats every 5 inches.
Fill the screw holes on the top of the desk with putty and let it dry. Sand the desk top, then paint it in the desired color.