Step 3: Mount the Pieces
Take a moment to figure out the alignment of the pieces, then glue them down so they don't move during the drilling (DRILLING!!!!!!).
To permanently fix the pieces to their new home, first drill a hole slightly narrower than your wood screws. NOTE, don't try to drill through the plastic spacers (yes, this may have been part of the reason my drill bit got stuck...). Also, try not to run out of super glue right before your drill unglues the stacks of plastic and splits your carefully measured, cut, and sanded piece of wood in half, thus necessitating the use of more glue, which you of course don't have because you just ran out.
Once the holes are in place, you can drive your screws in (using your powered screw driver, OF COURSE).