The student pilot stated that he was conducting a "normal" landing to runway 32. During the landing flare, the airplane "seemed to float," and the airspeed "was getting low." The student pilot applied power, and the airplane contacted the runway and "pulled hard" to the left before exiting the runway into the grass. The airplane impacted a runway sign and traveled approximately 1,000 feet across several taxiways and grass areas before it impacted a parked airplane and came to rest. The airplane sustained substantial damage to the left wing. The student pilot reported there were no mechanical malfunctions or anomalies. Winds at the accident airport, recorded 23 minutes after the accident, were from 240 degrees at 11 knots, with gusts to 20 knots, and a Federal Aviation Administration inspector confirmed there were left crosswinds at the time of the accident.