According to the student pilot/owner, when he initially checked the weather 2 hours before takeoff, his intended route of flight was “cloudy,” but reporting visual meteorological conditions. After the student pilot and his passenger arrived at the airport, the student pilot checked the weather again and decided to fly southeast before proceeding direct to the destination through better weather conditions. After the student pilot took off, he requested flight following and informed an air traffic controller of his intended route of flight. The controller advised the student pilot of possible rain en route, and recommended that he modify his route of flight to proceed direct to his destination. The student pilot accepted the controller’s advice and found the first 45 minutes of flight to be “fine,” but the weather worsened. The student pilot flew into clouds "briefly" twice, but maneuvered the airplane back into visual conditions. He then asked air traffic control for advice, but all the suggestions “yielded no relief.” Shortly thereafter, the student pilot declared an emergency and decided to make an emergency landing to a field. The student pilot “dropped the plane down on the mains as firmly as possible, and [it] bounced and went airborne again.” The airplane traveled down the field, hit the top of a fence and continued up a hill, where it finally came to rest. The airplane incurred substantial damage to the forward section of the fuselage and the right wing root. The pilot did not report any mechanical anomalies with the airplane. The weather reported at an airport about 15 miles east, about the time of the accident, included broken clouds at 500 feet; broken clouds at 900 feet; overcast clouds at 1,400 feet; and light rain. The student pilot reported 170 hours of total flight time.