The math is:
Length in feet x width in feet x .5 (for 6" slab), then the answer is divided by 27 to = cubic yards.
If it is a larger slab, figure your whole "trench" (it's a footing) area this same way, right from the top to the bottom. You do it this way on a big slab (especially 6") because it is too easy to underestimate on a larger slab.
You can be more precise and calculate closer on a small slab...
If it is a small slab, figure your "trench" area only from 4" to 6" lower than the top of the slab to the bottom. In other words, don't count in most of the part that the 6" slab will be occupying above the "trench".
Backfilling: Just shovel the dirt up against the outsides of the boards, and let it go down into the gap... Stomp it in down there. Now pack it back into the gap from the inside with your hand or feet. If there is some still inside the form, shave it off neatly with a flat nosed shovel. If there are some cupped holes toward the outside, don't worry about that little bit of under flow... as long as you have a fair amount of dirt tightly banked up there to stop the concrete. The dirt, itself, will act like a form board.