Seeing as this is to fit in a compartment in my secretary desk, I measured the size I would need and cut out the net shape from some old cardboard that was lying around (the box I keep my ice-skates in, actually).
For each piece of cardboard, I cut twice the size of fabric. This box is 4" x 6" x 8" and I used exactly a fat quarter (18" x 22") for covering all the pieces (tiny seam allowances).
I then sewed up two of the sides to make a little pocket for the piece of cardboard. I found that a snug fit worked best, so I re-sewed a few of the seams so the piece of cardboard wasn't rattling around inside the pocket.
I did this for each piece of cardboard.
I then hand-sewed the remaining edge closed (the tighter the better). This was the time consuming bit, so I watched a movie while I did it... and didn't take any photos of that step.
I then sewed all the pieces back together to make the box.
I sewed all the sides onto the bottom first, and then just did a few little stitches at the top corners once I lifted up the sides of the box.
I was originally just going to tie a ribbon around to keep all the sides up, but realized they would flop to the inside if the box was empty.
Despite the time it took, I am very pleased with the results... still need to fix the bow though :)