I made no new purchases and only made use of whatever items I had on hand. You can modify the dimensions or materials to suit your needs.
Step 1: Materials
Materials I used to make a 2-panel, 36" x 18" Shoji screen:
4 pieces of cardboard (36" x 18"), the thicker the better. These pieces were all taken from a single moving box that I had. Cut carefully and make your edges as clean as possible. You can find free cardboard on Craigslist, if you live in the U.S. People that have recently moved or have bought furniture will usually be eager to get rid of their excess cardboard boxes and will list them for free.
12 pieces of onion-skin paper (8.5" x 11"). These can be purchased at any office supply store. You can substitute onion paper with rice paper, vellum, or any other semi-transparent paper. The semi-transparency will filter light and give it a nice glow.
3 Cable ties/Zip ties
Other items: ruler, fat color markers, pen/pencil, clear tape, box cutter, glue. I would've used Gorilla Glue, if I had any. ;-)