I tried to find a box that was close to the same size as the air filters I had for my house. A diaper box was close enough. I centered the filter with one edge and then flipped the top fold either out to extend or in to reduce the opening of the box. I took an old fan from an electronics cabinet, cut a hole for the blades and poked 5 holes in the cardboard for the screws and cord to go through.
The fan is rated at 110 CFM. If you had some muffin fans from some old desktop computers, you might want to use couple to get the CFM up a bit.
The air filter was about $2.50 from the hardware store. I don't think the cheap dollar filters would hold much of the fine litter dust. This filter was pretty full after 2 months. Significantly reduced the amount of dust on the surfaces in the room.