Draw a level line around the bay window walls at 30 inches up from the floor. Find the wall studs and mark their position on the level line.
Measure the length of the back wall of the bay window and cut a length of 2-by-2 to this length. If the bay window has angled sides, miter the ends of the 2-by-2 to fit the wall angle. Position this board under the level line on the back wall and screw in place with two deck screws into each stud. Measure and cut the 2-by-2 for the remaining walls and attach in the same manner to create the wall cleats, or supports, for the desk.
Measure the length of the bay window opening and cut another piece of 2-by-2 to this length. Position this piece of 2-by-2 in the opening, abutting the ends of the cleats on the side walls. Attach this cleat with two deck screws through the ends into the abutting ends of the side-wall cleats.
Measure the distance between the back wall cleat and the cleat across the opening, and cut two pieces of 2-by-2 to this length. Insert these planks, evenly spaced, between the front and back cleats, and secure in place with corner brackets and wood screws.
Measure the dimensions of the bay window recess to get the dimensions of the desk top, and cut out the top from plywood or MDF. Position the desk top on the cleats and attach it to the cleats with wood screws every five inches around the perimeter of the top.
Fill the screw holes with wood putty and let dry. Sand the desk top, then paint it and the cleats.