The fight instructor reported that on the first landing the pilot-rated student failed to extend the landing gear. The instructor further reported that he didn't notice that the landing gear was in the UP position on approach to landing, and that the pilot-rated student had set the manifold pressure at 15 inches; the landing gear warning horn is set to activate at 13 inches of manifold pressure. The flight instructor also stated that the landing checklist was not accomplished. The airplane landed with all three landing gear in the retracted position, which resulted in substantial damage to its undercarriage.