It's much easier to learn the principles with a trainer, but if you're willing to do lots of reading and experimenting on your own you can certainly pick it up. I highly recommend http://www.amazon
.com/Elements-Dressage-Guide-Training-Young/dp/1585747351/ref=sr_1_4?s=books&ie=UTF8&qid=1342594146&sr=1-4&keywords=dressage, which goes through a slightly modified version of the training scale Reno posted.
I've seen gaited horses at dressage shows before, but they were different breeds that still had a standard walk, trot, and canter. IIRC, the fox trot replaces the standard trot with MFTs, right? If that's the case, you may be limited to breed shows, if they hold them at all. You can still practice it at home, of course.