Unfortunately i didn't take enough pictures but what i did take hopefully you will be able to use as a guide.
First, my wife bought this four drawer table (1 narrow drawer, 3 deeper drawers) in white that we pretty beat up. so i used paint remover to remove the old paint and sanded it smooth. then i noticed a big gap between the last drawer and the bottom of the desk. The bottom of each drawer had a particle/ thick card board bottom below the drawer guide which was cut to fit into notches in the front and back of the drawer below the guide. i was able to bend that piece to the lowest drawer just enough as not to break it but still be able to remove it if i laid the desk flat on the floor. with that piece out i then removed the guide on the lowest drawer. it was stapled in the front and the back, which reminds me i also removed the back panel behind the 3 drawers. that too was made of the same card board like material. before i removed the lower drawer piece below the guide (dont know what its called, sorry) I drew a line where it slid into the notches and cut those pieces off (about 1/4" in the front and back)
After removing the guide and the back panel i was able to measure the length and width that i needed. I cut a piece of 1/4 plywood the size i needed and nailed it with a nail gun just above the decorative arch on the bottom of the side of the desk. this gave me a 6"-7" deep area below the bottom drawer that could not be seen. even laying down it looks like the bottom of the drawer area. I then glued and nailed the drawer guide to the particle/card board which i cut so it no longer slid into the grooves, it was now all one piece (that was exactly how it looked before i realized they were not attached). I found two tiny hinges in my scrap pile and stapled one side to the under side of the back of the particle/ card board that had the guide attached to it, i also applied some wood glue to strengthen the area that was stapled. I then found some small 1/4" screws that i used to attach the bottom of the drawer with the guide to the area that was originally used as a notch before i trimmed the particle/ card board. this allowed the guide to be lifted up without it sliding around causing the bottom drawer to not be well supported. I replaced the back with some thin plywood that i had laying around to cover the newly built compartment and painted every thing a flat black and applied 2 coats of semigloss poly.
Again i apologize for not having pictures during the process, i didn't know this contest was taking place. this is also my first instructable, i will try to add more pictures if my daughter hasn't used the compartment already. Any feedback would be greatly appreciated.