Question: If a person wanted to compete in any of those things with their dog, does the dog have to be intact, or can it be spayed/neutered?
Answer: Excellent question! And the answer is absolutely not! Spayed and neutered dogs are welcome in all events except conformation. The reason is that conformation competition is meant to evaluate breeding stock so all dogs must be intact. But all other events like obedience, agility, tracking and more welcome spayed and neutered dogs.
Question: Does my dog need to be AKC registered?
Answer: Again, only for conformation competition. All other events will allow dogs that are clearly an AKC registrable breed but do not have a pedigree (a list of parents, grandparents, etc.) to back up that claim. If you have a dog that looks like a certain breed but you do not have paperwork for the dog from the AKC, you must apply for a special certificate called a Purebred Alternative Listing (PAL). This was previously called the Indefinite Listing Privilege (ILP). Once your dog has a PAL number, you can compete in any number of sports like obedience, agility, earthdog, herding and more!
Question: How does one get involved - join a club, or contact someone who works in general dog training?
Answer: I would suggest you seek out your local dog training club that hosts AKC events. Most of the time you don't have to join the club to take the classes (though it might get you a discount on classes). Choose a sport you think you might like, take a beginner class and see how you like it. The class will teach you what you need to know to enter the first level of competition. (Or it should, if it doesn't I would wonder just what goals the club has for students. I know some trainers around here not affiliated with the local club will make you go through 3 or 4 $100 classes before they teach you everything you need to know! That is ludicrous!) Download the rulebook for the sport at the AKC (or whatever venue you choose) website for free so that you can refer to them when you have questions outside of class. Join a yahoo group that focuses on the sport of your choice and introduce yourself. Groups are a fantastic place to ask questions, get immersed in the particular activity and get info you might not get anywhere else. If you aren't sure about what you might like to do, a general obedience class (not puppy or companion obedience but a true novice class) would get you started.