Measure the cabinet opening horizontally and vertically.
Measure across the longer edge of the plywood to the vertical measurement plus 1 inch and make a pencil mark. Measure across the perpendicular edge of the plywood to the horizontal measurement plus 1 inch and make a pencil mark. Repeat using the beadboard.
Place one leg of a framing square against the edge of the plywood with the corner at a pencil mark and the other leg extended over the surface. Trace the edge of the square across the plywood with a pencil to make a line. Repeat on the perpendicular edge at the other mark to make another line. Repeat using the beadboard.
Align a yardstick with a pencil line on the plywood. Trace its edge with a pencil to extend the line. Use the yardstick in the same manner at the other line to make the two lines meet. Repeat using the beadboard.
Cut the plywood and the beadboard at the lines using a circular saw. Sand the rough edges of both pieces.
Pour wood glue into a small paint tray. Roll the small paint roller through the glue several times to saturate the foam. Set the plywood on a flat work surface. Roll a thick coat of glue on one side of the plywood and on the back or plain side of the beadboard. Let the glue dry until it is tacky or sticky.
Set the beadboard on top of the plywood with the glued sides together. Cover the beadboard with a sheet of craft paper. Iron the paper with a medium iron. Set flat, heavy objects, such as encyclopedias, on the beadboard door for 24 hours.
Remove the objects and sand the dried glue off the edges of the door.
Choose the location for your cabinet pull or knob on the edge of the door that will open. There is no rule that governs pull location. Set one pull on the door and mark the screw hole location on the door with a pencil. Drill the bolt hole through the door at the pencil mark. Slip the bolt through the hole from the back side. Set the pull on the end of the bolt and twist to tighten them.