The Internet boasts a variety of free instructional videos to help get you started, including Learn to Dance and others (see Resources). In the videos, experienced dancers guide you through different steps and moves.
Check nearby colleges' course schedules online or pick up a current course schedule from the admissions office. Colleges and community colleges often offer contemporary-dance classes to nondegree students; stand-alone courses sometimes fall under the category of "Continuing Education."
Look for classes in nightclub dancing from private instructors in your area through websites like Eventful, online classifieds sites and your local newspaper's classifieds. However, before attending a class you find online, research the instructor. This could mean asking her a few questions about her training and experience or talking with members of the class beforehand.
Whether you join a class or opt for the video method of learning to freestyle dance, practice at home to music you like before going out on the town. Learning with a partner can make it twice as fun, so if you have a willing friend or significant other, ask her to learn along with you or offer constructive criticism.
Bring a friend or two to a nightclub where you will feel comfortable. When you arrive, relax with friends first and take in the atmosphere. Observing other dancers' moves can provide ideas for dances you might want to try. Most importantly, enjoy yourself---your confidence will shine through.