Establish level lines near the floor all the way around the walls. The highest point being 5 1/2" or slightly less from the floor. Decide which direction you want to run your floor joists based on ease of installation of the duct work.
Stretch a string exactly where a floor joist will placed from the level line on one wall to the other. Measure down every foot from the string to the floor and write it down. Now is the time to decide if 2x6's will work. You may need wider joists to make the ductwork fit. Go buy the materials now. Transfer those measurements to the 2x that will be used as the floor joist. cut the excess off and lay it in place. If it isn't touching the floor, step on it and check it by the string. You may need to place a shim here and there. Use glue and Concrete fasteners. It doesn't really matter what type you use.
I hope this helps!