There are three state forests in Florida that offer OHV-dedicated trails: Tate's Hell, Blackwater River, and Withlacoochee. To ride in these areas, you'll need to grab a permit from the location you're visiting. In addition, you can find ATV parks and rental agencies that will let you experience the thrill of off-roading.
Check out these Fort Lauderdale, FL ATV/OHV resources: