Positive reinforcement dog training rewards dogs for doing what you want them to do. Rewards usually take the form of a treat or praise, although sometimes people use toys or 'play time' (with you or with other dogs) as a reward too. Dogs learn "manners" (and really, any behavior) when that behavior is somehow reinforced. Positive reinforcement dog training does this by making the dog want to repeat the behavior in order to get the reward. This is a humane training method that helps to strengthen your bond with your pet.
In contrast, punishing a dog for bad behavior can lessen or even destroy the bond with your pet. It teaches your dog to be afraid when you're around, and can actually cause inappropriate behaviors such as biting or snapping.
Dog obedience training should be positive, upbeat, and fun for both you and your dog. Many dogs are food-motivated so bring a small bag of tasty tidbits to use as a reward (note: be prudent about how much you feed... these are extra calories, which can contribute to weight problems! Use tiny but tasty treats).
One important key to successful training is immediately rewarding your dog when he does what you want him to do. Timing is crucial; reward him the instant he responds to your command so that he associates his behavior with the reward.
For example, let's say you are teaching your dog to sit. Once you give him the command and he sits down, immediately reward him (even if you use treats as a reward, also use verbal cues - "good dog!", said in a happy voice). Don't wait too long to reward him... if you do and your dog gets bored, he may jump up to go elsewhere, and you've just lost the opportunity to positively reinforce the "sit" command. The dog must be rewarded while he's sitting (or doing whatever behavior you asked of him) - if he sits then pops back to a standing position, don't reward him or you'll be rewarding the act of standing up. Remember, the timing of the reward is absolutely crucial!
Consistency is another key to successful dog training. Until your dog knows the command very well, make sure you always reward him instantly for responding. Once he's reliable, reward him when he continues to "hold" that command until released. For instance, when you tell your dog to "sit", he should remain in sitting position until you give him a release word.
Many dog training classes are available to help owners figure out what to do. These classes are fun and upbeat and gives both the owners and their dogs a chance to socialize while learning. Read the article, How to Find a Dog Trainer that's Right for You. for more information.