Sweep the dust and debris from the surface of the concrete slab. Install a vapor barrier over the clean concrete surface by cutting enough strips from the vapor barrier to cover the entire slab and using the adhesive on the backs of the barrier strips. Overlap all of the strips by about 6 inches and line the seams with plastic tape.
Measure along each edge of the concrete slab. Cut a 3-inch wood board to the size of each side and set them on the floor along each side. Drive 4-inch concrete screws through the boards and into the slab below every 6 inches.
Measure the distance between two of the edge boards that sit opposite each other on the slab. Cut enough 3-inch boards down to this length to place a board every 12 inches across the floor, creating joists. Use 4-inch screws every 6 inches to secure the joists as you did the edge boards.
Place ¾-inch plywood panels over the floor joist addition that you built onto the top of the floor. Use enough panels to cover the entire floor, cutting the joists down as necessary. Use 3-inchs screws every 6 inches along each joist that a panel touches to secure the panel to the joists.