This wasn't free to build, but depending on what you find, you may be able to make it for close to free. I spent about $100, total.
This instructible is more of a "duh, why didn't I think of that?" kind of thing, rather than something really creative. But my kids were impressed, so I decided to share.
Step 1: Supply List
Small battery operated, motion activated light
Rubber door mat with "nubs"
Step 2: Put Things in and Check Fit
I decided to cut my door near the back of the box's right side. The litter box (I have one of those large ones) sits all the way to the left inside the box.
Step 3: Cut a Cat Door
the deck box I purchased has vertical stripes of two different textures, so I used two of them to assist in my vertical cuts. Start by just scoring your desired cut, then go back over your scored line with more pressure. Two or three passes should have you pretty well through the plastic of the box. The only difficulty will be where there is a thicker stability bar molded in - just take your time and you'll be through those thick parts in just a few more passes.
After making my two vertical cuts, I again used the box's decorative textures to decide where to cut. In the case of my box, the hole came out to be 5" wide by 8" tall. I wasn't sure that would be enough for my plump cat, but she walked in just fine, as did my tall cat.
Step 4: Finish Up
Using double-stick tape, adhere the motion-activated light to the inside wall of the deck box fairly high, and in about the center of the back wall, so it will both pick up the motion of a cat entering, and will stay on while he/she takes care of business.
Put anything else you plan to store in there. Find your cats (in my case, they were all lying around watching me work). Put the bravest one in the deck box through the top, and let him/her explore. Kona looked around a little, rubbed his head on the nubby floor mat, and popped right out the cat door. My two ladies followed, and all of them seemed quite content with the setup right away.
The last step I took was to put one of those sticky litter catcher mats (Wal-Mart, pet section, just a couple of bucks) on the floor outside of the cat door, to hopefully grab any remaining litter that doesn't get scrubbed off by the nubby mat inside the deck box.
Step 5: Final Thoughts
There are dozens of types of deck boxes out there, from ones that seat just one person to some that are nearly five feet wide. Consider the location where you want to have your litter box enclosure, and make your decision accordingly. There are, of course, deck boxes that don't incorporate a seat, but I kinda wanted one I or the cats could sit on, and tried find one to match the color of my bathroom as much as possible.
I bought a second nubby door mat, which I plan to cut, back with 1-inch foam blocks, and adhere to the inside of the deck box so the cats can rub up against it - they seem to really love the texture. The foam blocks are because the inside of the deck box incorporates the thicker structure bars, so the flat surfaces are recessed. I will just mash a piece of foam against a wall to make an impression of the structural bars, then use my box cutter to carve out those grooves so the foam will sit flush against the solid surface and stick well.