The pilot was conducting takeoffs and landings in the airport traffic pattern to familiarize himself with the tailwheel-equipped airplane, with a second pilot who did not hold a flight instructor certificate. At the suggestion of the second pilot, the pilot attempted to perform a "wheel landing," and during the landing roll, the airplane veered to the left. The pilot attempted to correct with aileron and rudder inputs, and the airplane nosed over and subsequently came to rest inverted, resulting in substantial damage to the wing spar and vertical stabilizer. The pilot reported there were no mechanical anomalies that would have precluded normal operation of the airplane, and stated that he had no prior flight experience in the accident airplane make and model.