The student pilot stated that he was given a clearance to climb out to the west after taking off on the last leg of a three-leg cross-country flight. He departed at 3:35 local time, with 26 gallons of fuel on board. He stated that by the time he was able to turn onto his course heading he was off his planned route of flight. He reported that the haze and setting sun made it difficult to see and that he was not able to locate his checkpoints to get back on course. After flying around in order to attempt to identify his visual checkpoints, the engine experienced fuel exhaustion and the pilot performed an off-airport landing to a dark area in the terrain; however, the field was short and the airplane contacted trees and nosed over during the landing flare. The airplane sustained substantial damage to the wings and fuselage.