The student pilot and his instructor were landing in a tailwheel-equipped airplane at night. The student pilot did two full stop landings on the night cross-country flight. During the first landing, the airplane stalled just above the runway, and the front left landing gear made contact with the runway first, resulting in a hard landing. The second landing was a normal, soft touchdown landing. A postflight inspection revealed that a portion of airplane's fuselage, on the left side, sustained substantial damage from the hard landing. The instructor pilot stated that there were no preaccident mechanical anomalies with the airplane that would have precluded normal operation.