Measure the width of the space underneath the desk with a tape measure. Cut two sheets of 1/2-inch-thick plywood to the length measurement and 8 inches in width with a circular saw. Cut another sheet of plywood to the length measurement and 4 inches in width.
Connect the two 8-inch-wide plywood sheets at right angles to one another to form an “L” shape. Use a drill with a screwdriver drill bit and one countersunk, 3/4-inch-long screw per foot of length along the joint. Screw the 4-inch-wide plywood sheet to the end of one of the 8-inch-wide pieces at right angles and use the same number of 3/4-inch-long screws as before.
Stand the U-shaped structure you have built so there is one 8-inch-wide piece and one 4-inch-wide piece standing vertically. Screw three L-brackets to the open end of the 8-inch-wide vertical piece so there are L-brackets 3 inches from either end of the piece and one L-bracket in the middle of the piece. Screw the tray to the underside of the desk with the L-brackets.