The certificated flight instructor (CFI) stated that he was the pilot-in-command and safety pilot because the other pilot had not flown in about eight months. Preflight inspection of the airplane revealed each fuel tank was half full, which was adequate for the planned one hour flight plus a reserve. After takeoff, the flight proceeded to another airport, where two uneventful touch-and-go practice takeoff and 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 right tank to supply the engine. The engine operated 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 subsequently experienced a total loss of power. During the descent, the CFI switched to the right tank again. The engine did not regain power and the performed a forced landing to a grassy hill. During landing, the nose gear sheared and one wing incurred substantial damage. At the time of the airplane's wreckage recovery, no fuel was noted in the left tank and about eight gallons of fuel was drained from the right fuel tank; 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. The CFI opined that the engine lost power due to the left tank becoming exhausted of fuel, which 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 three seconds.