I'll shot you some images of the one I built for my mother.
No you don't need a slab, a good bed of crush-a-run or pea gravel is ideal. There is a clear plastic roofing, similar to tin roofing and sold in home stores. I knocked together a small stick frame shed, covered the north wall and its two common corners with siding, and used the corrugated plastic on the roof and south wall, a storm door for access. The corrugated plastic is sold with roof caps, same as with tin roofing, and shaped strip insulation to plug air holes.
For a temporary green house, when we used to own a nursery we would make them out of large aluminum hoops and plastic roll sheeting. We would prepare a bed of gravel for the floor, and then erect the hoops (acted as tent poles) and cover them with two layers of plastic roll sheeting (equates to the fly of a tent). Plywood was used to cap the ends and a storm door was cut into one of the plywood end walls.
We used two layers of plastic because inside the greenhouse we would cut a hole in the first layer of the sheeting and install a bathroom fart fan so its exhaust would fill the gap between the two sheets like a balloon. This gave a layer of dead air for insulation. Cheep, quick to build and quick to tear down/move.