A kitchen oven or some other way of heating plastic. (Don't use a heat gun; it's hard to heat a non-tiny sheet of plastic evenly with a spot-heating device like a heat gun.) If you want to build a small standalone vacuum forming oven cheaply, check out my $30 oven design at www.rcgroups.com: http://www.rcgroups.com/forums/showthread.php?t=621858
A good vacuum cleaner, preferably a powerful (1000 watts or more) canister vacuum. If you don't already have one, you can get one for $5 at the Goodwill Outlet Store (a.k.a. Blue Hanger Store). Don't buy a shop vac just for vacuum forming; they don't suck any harder than a high-wattage household vac, and they're bulky. (If you already have a shop vac, though, you can go ahead and use it.) Don't buy a new canister vacuum, either; the centrifugal pumps in vacuum cleaners don't have seals that wear out, so a used one that works is fine; it'll suck as hard as a brand new one costing 20 times as much. (If the filter or bag is dirty, just take it out; you don't need a filter. If a few particles do get sucked through it, they won't hurt it; centrifugal pumps are nice that way.)
A 3/4" MDF (medium-density fiberboard) board at least 2 inches bigger than the inside dimensions of your oven, cut down to 2 inches bigger each way. If you have a big enough scrap board around---maybe a piece of plywood or thick particle board---it will probably do. It needs to be pretty smooth on one side (the top). (MDF will cost about 5 dollars for a 2 x 2 foot sheet, or about 9 dollars for a 2 x 4 foot sheet at Home Depot.) You can substitute a scrap board you have lying around (such as 1/2" or thicker plywood), but it should be smooth on the top side. (MDF is nice and smooth.)
A 3/4" galvanized floor flange (plumbing fitting). (Less than $3.00.)
A 3/4" x 2" threaded pipe nipple (or "riser"); PVC plastic or galvanized is fine. (That's just a short piece of pipe threaded on both ends, about 50 cents.)
A little PTFE tape, a.k.a. "Teflon tape," used for sealing plumbing joints. (About $1.)
Four 3/4" long wood screws, fairly large diameter but small enough to fit through the holes in the floor flange. (About $1.)
8 aluminum windowscreen frame corner braces, for 7/16" or 3/8" thick frame material. (5/16" will do for small frames and thin plastic, but thicker is better for larger or thicker plastic; small differences in thickness have a significant effect on stiffness). You want aluminum corner braces, not just plastic ones that fit aluminum frames. I use 3/8" corners from a local True Value (25 cents each) with 7/16" frame material from Home Depot, and that works fine.
2 or 3 sticks, 6 or 7 or 8 feet long, of aluminum 3/8" or 7/16" windowscreen frame material that goes with the aluminum frame corners. You'll need enough for four frame sides in each of the two dimensions of the plastic you'll be using, plus a couple of inches extra per stick. (About $4-5 per stick.)
1 box of a dozen binder clips, large size, from an office supply store. (Three or four dollars.)
A sheet of thin plastic 2" bigger each way than your chosen plastic sheet size, or just 1" bigger in a pinch, maybe a flimsy GARAGE SALE sign or a piece of the thin plastic you intend to vacuum form. (See step 7.) Unfortunately, Home Depot's big (14 x 19) signs are not flimsy or cheap, but Lowe's has 15 x 19 signs for $3. (Wal-Mart has them for $2, and smaller ones for $1 or so.)
A little silicone caulk or silicone sealant, or maybe epoxy, or rubber cement. (Any kind of gap-filling glue will work, if it doesn't set extremely quickly like hot glue. Tacky putty will do temporarily, in a pinch.)
A 10-foot roll of foam rubber weatherstrip, at least 1/4" thick and 1/2" wide, preferably 3/8" thick and 3/4" wide. You want the kind that's just foam rubber self-stick tape with a rectangular cross-section. (Three or four dollars at Home Depot.)
Some washers or coins to use as spacers.
Masking tape or (preferably) blue painter's tape.
Duct tape may come in handy, as it often does. (See Step 8.)
Some aluminum window screen material is also nice to have, but optional. Screening from a junked window screen is fine.
The main thing on this list that you likely won't find on a trip to an office supply store and a Home Depot is the aluminum window screen corner braces. (Home Depot and Lowe's only seem to sell plastic ones these days.) If you're not in a hurry, or can't find them locally, you can buy the frame corners online, and wait a few days for them to be delivered. http://www.Builderdepot.com
sells a tub of twenty 3/8" frame corners for $6. (Having extra corners is nice, so that you can have some different-sized frames without having to take them apart and reassemble them when you switch sizes.)
Another option is to make your frames out of wood. That's not my favorite way, but it does work---you can use wooden frames for a vacuum former, and many people do. (They'll eventually char and/or warp, but they won't catch fire in the oven; they won't be in a hot enough oven, or not for long enough.) If you're in a hurry and especially if you have the scrap wood around, that may be the way to go, at least to get started. I won't discuss wooden frames any further, because they don't get you the mix-and-match size advantage, and tend reduce the maximum size that will fit in a kitchen oven, but if you want to pursue that option, see this thread on www.tk560.com: http://www.tk560.com/phpBB2/viewtopic.php?t=466&highlight=draft+++simple+former
My Lowes doesn't sell small sheets of MDF, or thick weatherstrip 3/4" wide, so if you want to only hit one home improvement store, try Home Depot first.
You should probably take your vacuum cleaner hose to the store, and look for a plumbing fitting that adapts 3/4" pipe threads to roughly the size of your hose (inside or outside). It doesn't have to fit well, but anything that gets you closer is good. (See Step 8.) If you already have a shop vacuum with a large hose, and will be using that, you'll want an adapter from the large hose size to the small hose size. (About four dollars.)
While you're at the store, you may want to pick up a 2 x 4 sheet of textured styrene, sold as a fluorescent light diffuser panel for suspended ceilings. It's fun stuff to vacuum form. (Acrylic panels are nice, too, but a little trickier to heat and form.)
You'll also need some basic tools:
(1) a drill and a reasonably large bit (such as 1/4"), plus a bit that's somewhat smaller than your screws
(2) a screwdriver that fits your screws
(3) an electric saw such as a portable jigsaw or circular saw, unless you have the board cut to size at the store. (That's usually free; see Step 3.)
(4) a hacksaw
(5) a miter box you can use the hacksaw with
A portable jigsaw is good to have, but not strictly required. A hole saw (drill attachment) that can cut a 1 1/2" diameter hole is also nice, but not necessary.
If you make your frames of wood, you won't need the hacksaw, and maybe not the miter box.