Good introductory reading is Jarrod Jablonski's Fundamental of Better Diving. He goes into the equipment configuration, and the reasons for it, in great detail in the book, as well as discussing the other concepts of DIR diving, like standard gases and a team approach.
The basic approach to equipment is to keep things as simple as possible and still allow the functionality that's required. This minimizes failure points and allows massive standardization across a lot of diving environments. (It also makes the gear pretty darned easy to adjust, use, and maintain!)
Reading is great, but the best way to learn about DIR diving is to dive with DIR divers, because the honed situational awareness and team approach are something you really can't understand until you experience them.
For people who already have reasonable dive skills, the Fundamentals class is the entry point to the system (for GUE). It can be taken in a single tank, and it is an extremely good class, even if you don't go on to adopt the system, or take training with other organizations.
GUE and UTD do not use dive computers for either NDL or decompression diving, and Jarrod has a list of reasons why in the book.
Please feel free to PM me if you have any specific questions I can help you answer. I am both GUE and UTD trained, so I can talk a little about both agencies (although, as Tim observed, UTD is not really a good option in Florida).
Edited to address some of saxplayer's points: DIR is not the only way to dive with good skills and good trim. You can get those things from good instructors in a variety of places, and certainly in the cave community, which is pretty accessible to anybody in FL. The things that make DIR diving different, and may appeal, are the standardization of equipment, gases, techniques and protocols, and the emphasis on team. Achieving those goals requires commitment and does reduce your personal choices. Many of us have found that that is not really a problem -- AND although you have to meet certain requirements for the classes, there is nothing to say that you can't make other choices afterwards (although they will not be "DIR" choices).