The certificated flight instructor (CFI) stated that he was the pilot-in-command and safety pilot because the other pilot had not flown since November 2009. Preflight inspection of the airplane revealed each fuel tank was half full, which was adequate for the planned 1 hour flight plus reserves. After takeoff, the flight proceeded to another airport, where two uneventful touch-and-go landings were performed. The pilots then elected to return to the original departure airstrip flying about 800 feet above ground level. During the return flight, the CFI noticed that the single fuel gauge, which only indicated fuel quantity from the selected tank, indicated less than one quarter tank of fuel remaining in the left tank. He then selected the fuel from the right tank; however, the engine ran normally for "less than a minute" before beginning to “sputter.” The CFI immediately switched back to the left fuel tank, turned on the electric fuel pump, and applied carburetor heat. The engine regained power and the airplane began to climb, but the engine then lost all power. During the descent, the CFI switched to the right tank again; however, the engine did not regain power, and he performed a forced landing to a grassy hill where the nose gear sheared and one wing incurred substantial damage. During the recovery of the airplane, no fuel was noted in the left tank, about 8 gallons of fuel were drained from the right fuel tank, and there was no breach of fuel lines or fuel tanks. The fuel strainer contained fuel; however, there was no fuel at the fuel selector valve located in the cockpit or in fuel lines from the fuel strainer to the engine. When asked why he thought the engine failed, the CFI stated that he thought he ran the left tank dry and introduced air into the fuel supply system. A subsequent ground test indicated that with the electric pump on, the supply system should have been purged of air in about 3 seconds.