The student pilot stated 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 stated that by the time he was able to turn onto his course heading, he was off his planned route of flight. He stated that the haze and setting sun made it difficult to see, and he was not able to locate his checkpoints to get back on course. The pilot stated that while he was getting help from his flight instructor, the engine experienced fuel exhaustion and he performed an off airport landing. He stated he chose a dark area in the terrain on which to land; 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.