The pilot reported that they were conducting a "familiarization/instructional flight" in the retractable-gear airplane and that this was his first flight with the instructor. After practicing commercial maneuvers, they entered the traffic pattern, and the instructor wanted to acquaint himself with the "Johnson bar"-style landing gear system. The "Johnson bar" (manually operated retraction/extension handle) is pulled up to extend the landing gear and pushed down to retract the landing gear. The instructor then pushed the Johnson bar down in what he thought was the landing gear extended position. The pilot added that, although he twice verified that the landing gear was extended, the airplane landed with the landing gear retracted. The airplane sustained substantial damage to the fuselage. The flight instructor reported that the flight was briefed as a "familiarization" flight because he was unfamiliar with the airplane. He added that the pilot had time in the airplane, and the intent was for him to become familiar with the performance and limitations of the airplane before he began conducting commercial training for the pilot. He added that he became distracted with the operation of the flaps and did not verify the landing gear position indicator lights located on the left side of the cockpit. He also added that he did not hear the gear warning horn. The pilot and flight instructor reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.