Measure and note the width and depth of your cabinet space. Decide what height you will install the pullout tray. Mark the back and side inner walls of the cabinet at the height that the tray will be installed. Draw a horizontal line that extends across the back and both sides of the inner walls of the cabinet at that level.
Measure, mark and cut two 1-by-4 inch planks so they are 1 inch shorter than the depth of the cabinet from front to back. Measure, mark and cut one plank 1 inch shorter than the width of the inside of the cabinet. Draw a center line down the middle of each trimmed plank from end to end. Drill four evenly spaced pilot holes through the center line on each board. Precise positioning of the pilot holes is not necessary.
Position the plank to be installed on the posterior wall of the cabinet on the cabinet wall. Align the top edge of the plank to the horizontal line on the inside of the cabinet. Use a drill to screw the plank to the back of the cabinet. Install the side planks to the side walls with the same method.
Subtract 1/2-inch from the width and depth of the cabinet space to calculate the size of the pullout shelf. Measure and mark a sheet of 1/2-inch finished plywood to those dimensions. Use a carpenter's square to mark the board to ensure that the corners meet at 90 degrees. Cut the plywood sheet to size. Round the edges of the board with a router if desired. Sand the board smooth.
Mark the center of the front edge of the plywood that will be nearest the cabinet door when the pullout shelf is installed. Measure and mark the upper surface of the shelf 1-1/2 inches from the center of the front edge. Use a drill and a 1-inch spade bit to drill a hole through the board at that point. The finger hole will serve as a handle for sliding the pullout shelf.
Set the pullout shelf on the planks screwed to the inner walls of the cabinet with the finger hole near the cabinet door. Although the shelf is well supported, it may shift slightly from side to side as you pull and push the board but will not fall.