You can use the same kind of contact cement as you would use to apply high-pressure laminates to plywood when making countertops for your kitchen. The non-flammable kind is recommended. Paint it onto the areas to be glued, allow it to dry, and then press the pieces together. Just be careful to get the pieces lined up properly. You can put a piece of paper between the dried, glued areas and then pull it out when they're lined up.