I happen to own a kit car. It’s a 1960 VW bug which sometime in the late 70’s was converted to look like a 1929 Mercedes. The kit was called the Gazelle, and it was meant to look something like a Mercedes type S, although it is not identical to the original. If you look at old pics you’ll find there were numerous variations on the type S, so it’s not like there was only one version to compare it to.
Underneath the fiberglass it’s still a VW, so if you open up the mercedes hood there’s a trunk underneath, and if you open up the “trunk” there’s the engine. It has a mercedes type radiator grill on the front, but it’s just for decoration. VWs don’t have radiators.
Here are some pics: http://userweb.suscom.net/~sokosfamily/toy.htm
You can see the engine and trunk towards the bottom of the page and I threw in a couple of pics of the original mercedes S type to compare it with.
I happened to buy this kit car complete (although in much need of restoration), but many years ago I had looked into buying one as a kit. You have several options. You can buy just the kit itself, which is just the fiberglass, trim parts, etc. with no frame and no engine (you are expected to provide your own frame and engine from somewhere). You can buy a kit that includes the frame and engine. Or, you could buy the entire thing already built for you.
Volkswagen Beetles were very popular as the frame/engine for kits. You could also get the gazelle kit for a ford pinto, in which case the engine would be in the front. I’ve even seen one gazelle kit built on a mustang frame.
EBAY has a catagory for kit cars under EABY Motors. Most of the time these are cars that are already complete, but sometimes you’ll find unbuilt kits there. If you look there you can at least get an idea of the many different types of kits out there. Kits to make a modern-ish car (typically a Fiero or a Mustang) look like a 1950’s cobra are very popular. There are a lot of kits that allow you to make an expensive looking car out of a relatively cheap car, like Ferrari Diablo clones. There used to be a Hummer clone called the Bummer, but they were forced to stop selling it after they got sued by the Hummer folks. They still make the kit, but it’s no longer called the Bummer and they had to modify it so that it doesn’t look as much like the real Hummer.
Some of the kits require much more mechanical knowledge than others. A lot of the VW kits basically just bolt easily on top of a VW frame (VW’s are about the simplest cars in existance). Other kits have instructions like “cut the frame in half and weld in an extra sixteen inch section” which obviously requires much more skills than simply bolting things together. For the simplest kits you don’t need a degree in auto mechanics, but you do at least need the skills of a decent back yard tinkerer. For the most complex kits, you need to be someone like Jesse James (of Monster Garage fame).
All of the kits I’ve ever seen have been fiberglass. I’ve never seen one that used sheet metal.