I lay my batting on my dining room table. I then use spray basting and smooth the backing over the batting. It seems to work better for me if I keep the backing on top where I can see it. After that's spray basted, I flip it over and spray baste the top. I usually pin around the very edges just because I never seem to get it sprayed all the way to the edge.
After that I take a shower because I have batting fuzz sprayed to my arms. Next, I mop the floor just in case, but I've never had a problem.