I can never quite mange to bake and lay the fondant on the cookies while they are warm. So here are a couple of things that I think makes working with fondant easier. I went to JoAnns and got a yard of heavy clear vinyl (12 gauge) and cut it into 12 inch squares. I grease the square with Crisco, wipe it off with a paper napkin, put some fondant on it, dust the fondant with a little corn starch, and roll the fondant with a silicone rolling pin. I cut out the fondant, using the same cutter I used to cut out the cookie. I let the cutouts sit for maybe 10 or 15 minutes, using that time mostly to roll out and cut some more. I find that leaving it sit helps with the handling, it dries a bit and is more manageable. The small vinyl square lets you peel the fondant off, like a label, it doesn't distort quite as much. I don't do very many cookies at a time, maybe a dozen or so before I start the process over.
I use thinned Karo syrup (ratio: 2-3 parts water to 1 part Karo) to adhere the fondant to the cookie. I brush it on with a fairly good size artist brush. This adheres the fondant to the cookie nicely. HTH