We enclosed part of a car port about 9 years ago. The slab had no vapor barrier previously, as we could see moisture condense on the carport during temperature changes. We put down a layer of heavy-weight polyethylene sheet over the slab then installed the floor joists, with fiberglass insulation between the joists. Plywood subfloor, then vinyl tile. No problems so far.
That was the easy part - you should hear the one about the laminate floor in the dining room!