The pilot reported that while on a cross-country flight, the fuel in the left tank was exhausted and the engine stopped producing power. The pilot attempted to restore fuel to the engine by switching to the right tank which contained fuel; however, realizing that he was too low to attempt an engine restart, he elected to perform a gear up landing to a field. The airplane’s fuselage and right wing sustained substantial damage during the landing. No other preimpact anomalies with the airplane were reported.