There is an ever-growing list of agility sanctioning organizations. The ones you’ll hear about most often in the US are NADAC, AKC, and the USDAA (see below for a more complete list of national and international groups). Each organization has its own rules and style. For example, NADAC courses are spread out and focus on speed. They often challenge the handler to send their dog through the course at a distance. USDAA courses are “tighter” and more technically challenging.
Most training schools are happy to allow you to attend and observe (leave Fido at home for this) a class or two to be sure the style of instruction fits with your beliefs. Dogs learn best through progressive reinforcement training; rewarding the dog for making the right choice and withholding rewards, or ignoring the dog for making an incorrect choice.
Unless you plan to keep your dog outdoors--and few of us do because it's not recommended--you'll need to teach your dog where to eliminate. Therefore, house training (also called housebreaking or potty training) is one of the first things you need to work on with your dog. Crate training can be a very helpful part of the training process. This includes house training as well as many other areas of training: