According to the student pilot of the Mooney M20C, he was returning to land at his home airport following a solo cross country flight. During the approach to the runway, there was a crosswind, and when the airplane touched down it bounced twice. After the third touchdown, the left wing rose while the right wing dropped, and the pilot "didn't straighten out [the airplane] correctly." The airplane subsequently departed the right side of the runway, and the right wing struck a sign. The pilot did not report any mechanical abnormalities associated with the airplane.