Actually, from the way you describe it, the end result you want is very easy to accomplish.
You need to look for a tutorial that teaches you how to make a shiny reflective surface, usually called "plastic buttons" and then just insert your art under the "plastic button." if you want it to have the same sort of curved effect, just warp your art sligtly and play with the lighting on the original artwork so it matches the lighting on the "plastic button."
Most "plastic button" tutorials teach you how to make spheres, but you could easily translate it into squares or whatever shape you want.