okay, easy fun question. YAY!!! lol.
schuzthund is a working dog sport designed by max von stephanitz as a way of testing german shepherds, but also other breeds abilities in tracking, obedience and protection. It consists of schutzhund 1 title, schutzhund 2 title, schutzhund 3 title. there are others but those are the basics. each title requires all 3 phases = protection, obedience, tracking. each level (1,2, or 3) is harder than the last, both for the handler and the dog.
the most common schutzhund breeds in order are the german shepherd, doberman pincher, belgian malinois, rottweiler, and giant schnauzer. that will vary depending on the area of the country and world you are in. There are also bouvier des flanders, pit bulls, presa canarios, dogo argentinos, american bulldogs, labs, chesapeake bay retrievers, and many more who occasionally train in the sport. there has also been a Jack Russel Terrier who recieved a sch III title.
where do they train and compete? everywhere. to find a club in your area take a look at this website....
http://germanshepherddog.com/clubs/index.htm
I can't speak for every club, but every club I have ever visited enjoys having people come to watch and learn. Most club trainers will be happy to answer any and all questions, as will the majority of the members. Just keep in mind that if you visit a club, the trainer will most likely be pretty busy training dogs on the field so most of your questions will have to be asked of the members on the side lines waiting their turns and watching. I also recommend the book "Schutzhund: Theory and Training Methods" by susan barwig and stewart hilliard.
I am more than happy to go into more detail on each phase, and each phase of each level if you would like.