It's a pretty new sport. The opportunities to compete are still limited but more and more clubs are hosting demos at their shows or sponsoring seminars or classes.
Currently there is some variety in what freestyle entails ranging from precision heelwork set to music, which I gather is the form seen in competition in the UK,to more dance-like routines.
For folks who haven't seen it, Freestyle obviously has it's roots in obedience, but the use of music and additional moves like spins, side passes, weaving etc. are designed to show the partnership between the dog and handler in a more expressive way. In some respects it is similar to sports like ice dancing where the pairs are judged on both technical and artistic merit, as well as sports like dressage where the quality of communication between horse and rider is reflected in the quality of movement seen in the horse.
In my own experience, when Patsy and I are doing obedience work we are aiming for a specific ideal set by the organizing body, in our case the AKC. When we are working on our freestyle moves I draw much more heavily on Patsy's natural moves, not only her own rhythm for the heel work, but also her own interpretation of standard moves. For example, most freestyle dogs learn to bow, but there are many styles of bowing from a quick bounce to a long, exaggerated downward stretch. (Patsy bows with one foreleg tucked, sort of like a circus horse). There are also times in training were she'll spontaneously do some cool looking move that I try to develop into something we can use. Her first version of weaving included a spin each time she went under my legs, her latest offering is circling around me moving backward. In obedience perhaps the most frequent lament is "Rover never did that before!", in freestyle it's "How can I get him to do that again?!"
And, of course I'd be happy to answer any questions if I can.
YouTube Video of Patsy and me and our old K-9 freestyle team.