There are two broad approaches to dog training. The old traditional way is based on negative reinforcement, but a more common approach today makes use of positive reinforcement. What's the difference? Negative reinforcement occurs when the trainer does something negative to the dog to correct undesired behaviour, or to prompt desired behaviour. Positive reinforcement is a technique that involves doing something positive to the dog in order to reinforce a desired behaviour.
An example of each in action can be found with heeling. Heeling is when a dog walks closely beside the trainer, on the trainer's left hand side. Negative reinforcement could consist of jerking the leash, attached to a pinch or choke collar, whenever the dog forges ahead or lags behind. Positive reinforcement, on the other hand, could come in the shape of luring the dog to walk by the handler's side with a treat - if the dog doesn't forge ahead or lag behind it gets the treat, which is pleasant and positive, rather than the jerk, which is uncomfortable and slightly painful.
The decision about choosing positive or negative training methods, in my experience, depends largely on the trainer's outlook on life and misconceptions about dogs. Some trainers want the sense of control that comes with negative reinforcement, or believe that force is an effective method of training, or think that if they lure the dog with treats or a toy the dog will only perform the task asked of it when it knows a treat or toy is present. They doubt that the dog will actually obey commands simply because the trainer gives them. Some trainers think that dogs should do what they're told because they're told to do it. Others think that the dog should do what they want because of a dog's innate desire to please. This is all hogwash.
Other trainers understand that dogs do what they want to do, and that the trainer's job is to make the dog want to do what the trainer desires. This describes President Harry Truman's thoughts on managing humans - he said that the art of management is to make people want to do what you want them to do. Some handlers simply cannot understand why we would punish dogs for not learning something quickly enough, and feel that the responsibility for results lies with the trainer. Many trainers simply do not want to punish dogs. The best reason for positive training, however, is that it works extremely well once you understand it.
The first step to understanding positive reinforcement is to consider it from the dog's point of view. A dog that is positively reinforced during training enjoys it; a dog who is negatively reinforced does not enjoy it, although he will probably tolerate a great deal of it. The idea behind positive reinforcement is that the dog will figure out that if it repeats the behaviour it will be rewarded in some way. The idea behind negative reinforcement is that the dog will figure out that if it repeats a behaviour (one that is unwanted) it will experience an unpleasant consequence. Positive reinforcement encourages behaviours while negative reinforcement discourages behaviours.
What is the result? If the dog is not smart enough to remember every bad move it's ever made, or to figure out exactly what the trainer does not like, it will be discouraged from trying things. Bad signals from a trainer may make it impossible for the dog to understand what he's doing wrong, and why he's being punished. The dog will tend to shut down. Even a highly driven dog will do worse with negative reinforcement than with positive.
With positive reinforcement the dog will try many things to get the reward, whether its a treat, play, a toy or praise. He will pay close attention in order to make the trainer give him the reward - and in this sense the dog will begin to think that he controls the game, essentially thinking "I can make this person will give me a treat simply by sitting". Anyone who has fed their dog scraps from the table knows exactly how quickly a dog can figure out something.
What's more, a dog that gets nothing but positive reinforcement will offer new and novel behaviours in order to get treats or praise. This is how many great dog tricks are born - the dog does something random, and the trainer catches the behaviour by reinforcing it.
The easiest test for positive reinforcement is teaching a puppy to sit. A negative trainer will put the puppy on a leash, hold the leash tight so the neck and head remain high, and then push the dog into a sit. A positive reinforcer has two methods. One is to simply wait, knowing that "sit happens". They watch the dog, and when it sits they say "Sit" and reward it. The other method is to hold a treat over the dog's nose, and slowly move it backward. The dog will raise it's head to follow the treat, try backing up, and naturally back into a sit, at which time the trainer says "Sit" and gives the dog the treat. With repetition the dog begins to equate "Sit" with the sitting motion and the treat, and quite quickly your puppy will sit on command.
Positive training requires patience, and there are special techniques that are fun and easy to learn. Overall it is safe, fun and enjoyable for the dog. More to the point, it's effective. Besides, who really wants to punish their best friend?