People love floating frames...and for good reason. They really highlight the artwork in a very unique way. One of the questions I get all the time is, "Can I mount my 1/8" foam core photo or watercolor canvas in one of your floaters?".
Lets begin by explaining how a floating frame functions normally. A series of channels (or rabbets) are cut into the front of the frame (as opposed to the rear in a conventional frame), and a stretched canvas on a wood frame (like an oil painting canvas) sits down into the front of the frame and is held in place with offset clips and 3/8" screws from the rear.
So what's the answer? There are a couple of solutions here depending on your DYI level. If the artwork is on an 1/8" board, you can hot glue the board into the floater where it sits on the rabbet or hot glue it to the offset clips from behind. It can also be taped from the rear across the offset clips with a durable tape like Gorilla duct tape.
The best solution (but most time intensive) for any photo or thin board artwork is to hot glue, wood glue, or rubber cement (depending on the material) the artwork to a 1/2" piece of board like pine or plywood. This will allow you to use the provided screws to fasten the artwork from the rear as intended. (If you're doing this, be sure to let us know so we can make sure the depths will match the material that you are using.)
Here is a great video showing some examples of how this can be done...