The student pilot was on the last leg of a personal cross country flight with one passenger when he radioed to an FAA air traffic approach controller that he had a "lack of fuel" emergency and requested a heading to an airport. The pilot was given a direction and distance, but he decided he was not able to glide that far. The airplane subsequently sustained substantial damage when it nosed over during a forced landing on marshy terrain. The pilot reported no mechanical malfunctions with the airplane in reference to the accident flight. The pilot was asked by the NTSB investigator if he purchased fuel prior to departure on the last leg of his flight, and he indicated that he did not but should have. According to the pilot, his passenger held a private pilot certificate.