Yes, those craft foam sheets in the kids' section. I use the black sheets since I cover the back and sides with black paint.
The brand is Scribbles (BLACK SHINY) 3-dimensional fabric paint. Normally you'd use it on shirts or whatever - it dries puffy/3 dimensional. But I spread it on like cake icing (usually with the side of a long pin). You might be able to use a paintbrush to smooth it out if you prefer, I haven't tried that method though.
I found photo paper (8x10 sheets) at my local dollar store! I use the glossy kind. The graphics turn out fab.
If you don't have a laminator (I use a Xyron machine), I bet you could use clear packing tape instead.
If you intend to sell the items you make, you must use copyright free images. Not all clip art is free for use for selling purposes. Just FYI.
All of my images are original and drawn by me to avoid that whole issue.
This method is a lot of work and often a *literal* pain (cutting out the laminated graphics hurts after a while!), but it turns out really nice in the end. The "beads" are super light.