During a practice hover autorotation, the helicopter touched down hard on the left skid. It subsequently experienced a dynamic rollover, coming to rest on its side. The certificated flight instructor (CFI) reported that the purpose of the flight was to conduct training for the student pilot (positioned in right seat). After a 1 hour 20 minute flight, the CFI opted to have the student practice hover autorotations at the airport the helicopter is based and where the flight was to terminate. After the CFI rolled the throttle toward the idle position, the student immediately raised the collective and did not input enough right pedal correction. The student additionally made an abrupt left cyclic input, resulting in the helicopter drifting left. The CFI assumed authority of the flight controls in attempt to arrest the high rate of descent and regain directional control. The helicopter stuck the ground hard on the left skid and rolled over. The CFI reported no mechanical malfunctions or failures with the helicopter prior to impact. The CFI stated that his total flight experience totaled 725 hours, of which 300 were accumulated while acting in the capacity of a flight instructor; the student had amassed a total flight time of 6.8 hours. The FAA Rotorcraft Flying Handbook states that as part of the technique for practice autorotation maneuvers from altitude, the pilot should "smoothly, but firmly lower the collective pitch control to the full down position, maintaining rotor r.p.m. in the green arc with throttle." To practice hovering autorotations, it instructs the pilot to "firmly roll the throttle into the spring loaded override position." It further states that, "as the throttle is closed, apply proper antitorque pedal to maintain heading" and "leave the collective pitch where it is on entry." It then instructs that "at approximately 1 foot above the surface, apply upward collective pitch control, as necessary, to slow the descent and cushion the landing," and notes that "usually the full amount of collective pitch is required." The manual lists one of the common errors of practice hovering autorotations to be the pilot's failure to "apply up-collective pitch properly, resulting in a hard touchdown."