This design was inspired by this: http://www.fringeneering.com/2012/07/vacuum-forming-on-mega-cheap.html but designed to be super easy to make using off the shelf parts and minimal machining. Instead of using laser cut or 3D printed parts, we will use toilet flange extenders, available at Home Depot to make the base and the clamp that will hold the plastic to be formed (disposable plastic plates work great).

You will need the following:

3: Closet Flange Spacer Rings (Home Depot has "Raise A Ring" from Sioux Chief Mfg. (model 886-RQ), but others might work. Some other types don't have as many holes and might benefit from drilling a few extra.)
4: 1/4" x 4" hex bolts
4: 1/4" x 3/4" to 1" machine screws with countersunk head
8: 1/4" hex nuts
1: 1 1/4" x 1/2" PVC bushing (should have a flange on one end to serve as a good gluing surface, the other end should roughly fit your vacuum cleaner)
1: 4" PVC clean out cover plate (has a small hole in the center that will be drilled out to more or less match the inner diameter of the bushing). A 5" clean out cover plate also works and is a little easier to glue (it overlaps more). You can substitute anything flat made of PVC that covers the flange opening.
1: 18" of rubber weather stripping (I used Frost King EPDM Rubber Weatherseal 5/16" wide, 1/4" thick).
1: Can of PVC cement (I used Weld On 790 Multi-purpose)

The cost of these parts (excluding the weather stripping and cement) is about $16.

Step 1: Drill Hole

First, drill out the center hole of the the 4" PVC clean out cover plate. Make it about as big as the inner diameter of your PVC bushing (make sure it is not too large so that the bushing doesn't have enough surface area to attach to).

Step 2: Glue Parts

Follow the directions on your cement to glue the bushing onto the cover plate (line up their respective holes). Next glue the cover plate onto one of the toilet flange extenders. Make sure that you glue it to the side without the countersunk holes. The countersunk holes need to be on the top so that the nuts used to attach the vertical guide posts (the 1/4" x 4" bolts) will not protrude that much. Use the attached bushing as a handle to enable good positioning of the cover plate. The 4" cover plate almost exactly fits in the flange hole so it is a little tricky. Use plenty of glue make sure there are no gaps.

I've also included pictures of a base made with a 5" cover plate.

Step 3: Finish Base Assembly

Use some rubber weatherstripping to make a circular gasket around the top rim of the base.

Depending on your vacuum cleaner and specific bushings, you may benefit from constructing some sort of gasket or spacer to ensure a snugger fit. I used some ShapeLok plastic to make the inner diameter of the bushing more closely match my vacuum cleaner tube.

Insert the 1/4" x 4" bolts into 4 of the 8 holes in the flange extender, and attach with nuts so they form the vertical guide rails that the carriage will slide down on.

That is pretty much all there is to it. Now you just need to mount a plastic sheet between the two flange extenders that serve as the carriage, and it is ready to use.

Step 4: Mount Plastic in Carriage

Cut out a circular piece of thin thermoplastic with a diameter about equal to that of the outside of the flange extenders. Cut out notches for the 8 bolt holes. I recommend making a template and using it to trace the proper outline on your source plastic sheet. Plastic picnic plates work very well as source material. Salvaged clamshell packaging and 1 gallon milk jugs are also good sources.

Sandwich the plastic between the two remaining flange extenders and clamp them together using the 4 1/4" x 2" bolts and nuts. Be sure to use a consistent set of holes so the carriage can slide down the guide bolts.

Step 5: Use the Vacuformer

Slide the carriage over the guide bolts and then place the object to be vacuformed underneath on the base. Depending on the size and shape of that object, you may want to make a slightly elevated platform with some holes drilled in it to raise it up and to provide multiple paths for air to be sucked out. However, many objects can be used without any further modification.

The carriage should be able to remain above the object simply by friction between the bolt threads and the edges of the carriage holes. Place the base on the end of a vacuum cleaner hose and then use a heat gun to soften the plastic sheet in the carriage. I've used a Wagner HT3500 on high at 1150 Fahrenheit but I'm sure other settings or other heat guns can work fine. Once the plastic looks soft (it should be smooth and droopy, and for some plastics the color might change), turn on the vacuum and lower the carriage down the guide rails until it contacts the rubber gasket on the base. At that point the vacuum will almost instantaneously suck all the air out and you are done.