Here is what I came up with.
Step 1: What you'll need
Staple gun - I got the cheapest one they had at the hardware store, but a bigger one might be helpful depending on the weight of your fabric. My fabric was on the heavy side, so I probably should have been using bigger staples.
Jigsaw - This you'll use to shape the plywood base to fit snugly into the suitcase.
Screwdriver - This can be electric or manual. It is not too hard to drive screws into plywood, but it is a lot quicker to use a power-tool.
Utility knife - to cut the foam
Suitcase - clearly, this is the most important part. I used a soft suitcase (well, semi-soft, I think it's made of cardboard-reinforce naugahyde). The original Sit Bags are made of hard suitcases, which may hold up better in the long term, I don't know. The rest of the instruction will assume you're using a soft case.
Upholstery Fabric - I used a heavyweight, vintage upholstery fabric, but you could really use anything. An old wool coat might be nice. If the fabric is lightweight, you may have to reinforce it with iron-on interfacing. If you have questions about this, you could probably ask at your local fabric store.
Foam - The main structure of your seat will come from the foam you use. The type of foam you get depends on your preferences, what is available, and how deep your suitcase is/how high you want the upholstery to stick up from the suitcase. The
Plywood - just enough to fit in your suitcase (should be slightly smaller than the case).
Muslin - This is optional. I used a base layer of muslin to shape the foam base-layer so that the corners take a softer look, but this can be done with the main upholstery fabric too.
Bamboo fiber - This is also optional. I used a top layer of bamboo fiber on top of the foam so that it's a little softer. Adding the bamboo fiber layer yields a seat with more give, as the foam tends to be a bit firm. I used two bags of the stuff. I used bamboo rather than cotton mainly for the eco-benefit, and the fact that it is anti-microbial (as I'm sure the suitcase I found in the alley is full of microbes!).
Plumbing fittings and nipple - For the legs, I chose to simply use 4 pieces of 1/2 inch by 3/4 foot steel nipple and the associated plumbing fittings. They are cheap and easy, and I think they look nice, though it would be nice to find some screw-on feet for the bottom of the nipple, which leaves marks on my carpet. I tried to find miniature claw-and-ball feet, but then I thought that might be a little over the top, so I left it simple.