I got one of the images to work, with an img tag, in preview anyway:
It looks like they went out and bought a shop vac, made or found a thin square box, cut a hole in the side of it and plugged the shop vac in there, and put that up on the box the shop vac came in. I'm guessing there's weatherstripping around the top edge, and likely pegboard over the top of the box, but I can't see that in this picture. And maybe not. Maybe the thin box is metal, and they're sealing the plastic directly to the top edge.
The top frame looks like 1/16" thick 1" L aluminum from the hardware store, with the horizontal part slotted at the corners, and the vertical parts bent 90 degrees. Probably pop riveted or screwed together where it comes back and meets itself. This is a common frame construction that's featured in Doug Walsh's book.
The black clips holding the plastic to the frame are manuscript binder clips from an office supply store.
I probably wouldn't do things quite that way.
First off, don't buy a new shop vac just for vacuum forming; it's a waste of money. Take a piece of craft foam to a good thrift store, and try out the vacuums by putting the craft foam over the hose end, and seeing which one sucks the foam furthest into the hose. Buy that one. Shop vacs are not usually superior to similarly-powerful canister vacuums for vacuum forming. (I usually use a small but powerful hand vacuum I got for something like $3 at a Goodwill Blue Hanger store. It actually sucks harder than the shop vac I'd bought. Don't repeat my mistake.)
Second, I'd probably make the frames out of aluminum windowscreen framing stuff, with aluminum corners. That's cheaper, and gives you rigid corners, and it's very easy if you have a hacksaw and a miter box. (The aluminum corners I use require mitered cuts.)
Third, I'd make a platen out of a board, maybe 3/4" MDF, with a hole in the middle and the vacuum attached to that hole. (I use a galvanized floor flange and nipple, but you can save a couple of bucks by just epoxying the nipple directly into the hole.) You don't need more than one hole if you're only making one object at a time. And if you do want a bunch of holes, you can layer a piece of pegboard over the one big hole, on spacers.
All of this is spelled out in detail in my draft "Chapter 2" over on tk560.com:
http://www.tk560.com/phpBB2/viewtopic.php?t=466
There's also other information in there, including various alternative ways to make frames, and pointers to other intros & more advanced vacuum former info.