You can add the fondant while the cookie is still warm, and it will melt to attach. Or, if you are like me, and can't do it all at once, just brush the back of the fondant with a tiny bit of water and it will stick to the cookie.
Adding buttercream, too, will make it a bit too sweet.
After the cookies cool down, brush them with a thin layer of corn syrup, and then attach the fondant ( using the same cookie cutter ). It works perfectly! 
This is a picture of my cookies covered with fondant.
Thanks to everyone who replied I will be making spider man cookies for next Satruday I will alo be making 3 cakes for this same party I have already made the cookies now I will decorate them they will be covered with red royla frosting and I wanted to use fondant for the eyes but didn't really know how to make the fondant stay on thank again for all the help couldn't do it with out you guys.
Molly2 
I am working on cookies right now I came on here to see how I can complete them yes you can use royal icing just then it down with water a tablespoon at a time I did mine about 4:00 this evening and they are almost dry the should be ready to decorate by morning
Molly2
I rolled out all my fondant and cut the shapes out with the same cookie cutters I was going to use for the cookies. I baked the cookies and made sure the use the same shapes as my fondant cutouts. As soon as the cookies came out of the oven, I placed the shaped piece of fondant on top and it just adhered. That rolling and cutting of fondant was a project and a half. I was glad I got it all done before I even started baking the cookies. I found rolling on parchment paper eliminated the need to dust the surface.
I have decorated NFSC with fondant and with MMF by putting it on just after the cookies come out of the oven. It stuck quite nicely but I found that it came loose after a while especially when biting into it? Am I the only one? I also found it hard to get the icing ready before the cookies come out of the oven - it was a race against time. I thought I might try RI next time...
I have decorated NFSC with fondant and with MMF by putting it on just after the cookies come out of the oven. It stuck quite nicely but I found that it came loose after a while especially when biting into it? Am I the only one? I also found it hard to get the icing ready before the cookies come out of the oven - it was a race against time. I thought I might try RI next time...
To my knowledge the MMF didn't come off the cookies; but mine were gifts, so I don't really know. It didn't come off the ones we ate here at home. Come to think of it, I cut the cookies with a knife because nobody wanted to eat a whole cookie at once.
The "race against time" is why I rolled and cut my entire batch of MMF first.
I give credit to cc's nalyjuan who helped me when I did mine.
I use a sugar glaze on top of my cookies and brush that with a little water to make the fondant stick. I prefer to do it this way because I can play and stretch the fondant a little to cover the entire top surface of the cookie.
My cookies slightly expand during baking so when fondant is placed right out of the oven, they will not match and I will see the surface of the cookie on the edges that aren't covered with fondant.
It takes more time when I stretch the fondant, but it gives the cookie a more finished look imho. This is just a matter of personal preference.
Little Linda has the process! Cut out all the fondant shapes first, and cover with plastic wrap. Then cut and bake the cookies. As the cookies come out of the oven, place the fondant cutouts ont eh cookies and they will adhere. Just do all the fondnat work first.
Here's a picture of my fondant all cut out and waiting for matching cookies.
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