When you need to glue veneer to plywood, the best type of adhesive to use is rubber cement or contact cement. This is a substance that can effectively hold the veneer to the plywood without any issues. To apply, spread the adhesive onto the veneer and the plywood, and then press the two surfaces together. At that point, use a heavy roller to roll over the surface so that the 2 pieces of material are pressed tightly together. You need to remove any gaps between the 2 surfaces so that they will stick together well.