Attach an appropriately sized masonry drill bit to the electric drill, following the manufacturer's instructions. The bit should be one size smaller than the size of the masonry screws you intend to use.
Mark the drilling depth onto the drill bit. Hold a screw against the cutting edge of the bit and wrap a layer of masking tape around the bit just above the head of the screw. Marking this depth will prevent over-drilling.
Place the plywood in the desired position on top of the concrete board.
Drill pilot holes through the plywood and into the concrete to the pre-marked depth. Place one pilot hole in each corner of the plywood sheet and additional holes at 12-inch intervals. Exert a slow speed and medium pressure.
Install masonry screws, or "blue screws" as they are commonly known, into each pilot hole, following the manufacturer's instructions.