Use a measuring tape to measure the width and depth of the nook in which you plan to install your desk. These measurements will give you the dimensions of your desktop.
Place the desk chair you intend to use in the nook area and sit down. Raise your arms to a comfortable height for the desktop and use the measuring tape to take the measurement between your arms and the floor. This will provide you with the height at which you should install your nook desk.
Cut a sheet of 1-inch plywood to the width and depth dimensions you took earlier using a table saw. You may choose another building material such as medium density fiberboard, pine or other hardwoods but these materials are often more expensive than plywood.
Cut three lengths of 2-by-4-inch hardwood to use as supports for your desktop. One of the boards should be equal to the width of the nook and the other two equal to the depth minus two inches.
Use a stud finder to locate the studs in the walls and mark their positions on the wall in pencil. Make your marks at the approximate height of your desk so that once the desk is installed the marks will be covered up.
Lay the piece of 2-by-4-inch hardwood cut to the width of the nook flat against the back wall of the nook so its ends are flush with the side walls. Align the top edge of the board so it is level at the desired height for the desktop. Secure this board in place by driving 3-inch wood screws through the board into the wall studs.
Position the remaining two pieces of 2-by-4-inch hardwood on the walls perpendicular to that on which you installed the first board, aligning the top and bottom edges of all three boards. The ends of the shorter boards should be flush with the face of the longer board. Secure these boards in place by driving 3-inch wood screws through them into the wall studs and then toe-nail additional screws through the corner joints with the longer board.
Slide your plywood desktop into the nook space and push it all the way in so the back edge is flush with the back wall. The underside of the desktop should be flush with the support frame you just constructed and the sides of the plywood should be flush with the side walls of the nook.
Secure the desktop in place by driving 2-inch wood screws down through the desktop into the support frame beneath. When finished you may choose to fill the screw holes with wood filler and, once it has dried completely, sand it down to a smooth surface.
Paint or stain your desktop as desired then cover it with a coat of clear varnish or polyurethane to protect against water damage. Once the paint or stain has dried, pull your desk chair up to your new nook desk and try it out.