The pilot reported that the purpose of the flight was an orientation for two potential student pilots. During preflight, the pilot estimated that the fuel tanks contained 10 gallons of fuel, which he determined would be adequate for the flight. After completing two traffic patterns, and climbing the airplane to the downwind leg of the third pattern, the engine lost power, and "surged" during the subsequent forced landing. The pilot requested an emergency landing to runway 13, but amended his request to runway 8 because the airplane was "too high." He subsequently determined the airplane was "too low" for runway 8 and touched down hard on a taxiway, and skidded to a stop in the grass infield. The airplane sustained substantial damage to the cabin floor structure, but the occupants were not injured. Examination revealed that the airplane contained no fuel, and the pilot reported that he had exhausted his fuel supply.