Positive reinforcement adds something to the situation to increase the chance of the behaviour being exhibited again (for example, giving a dog a treat when he sits.)
Negative reinforcement removes something from the situation to increase the chance of the behaviour being exhibited again (for example, releasing the tension on an uncomfortable training collar when the dog stops pulling on the leash).
Positive punishment adds something to the situation to decrease the chance of the behaviour being exhibited again (for example, growling at a misbehaving dog).
Negative punishment removes something from the situation to decrease the chance of the behaviour being exhibited again (for example, walking away from a dog who jumps up).
Most modern trainers say that they use "positive training methods", which is a different meaning of the word "positive" from that in operant conditioning. "Positive training methods" generally means preferring the use of reward-based training to increase good behavior over that of physical punishment to decrease bad behavior. However, a good trainer understands all four methods, whether or not she can put operant-conditioning terminology to them, and applies them as appropriate for the dog, the breed, the handler, and the situation.
Rewards
Positive reinforcers can be anything that the dog finds rewarding - special food treats, the chance to play with a tug toy, social interaction with other dogs, or the owners attention. The more rewarding a dog finds a particular reinforcer, the more work he will be prepared to do in order to obtain the reinforcer.
Some trainers go through a process of teaching a puppy to strongly desire a particular toy, in order to make the toy a more powerful positive reinforcer for good behaviour. This process is called "building prey drive", and is commonly used in the training of Narcotics Detection and Police Service dogs. The goal is to produce a dog who will work independently for long periods of time.
Some trainers believe that the toy acts as a positive reinforcer for the desired behavior, when in all likelihood the prey drive works on an entirely different level from standard training and conditioning techniques. This is seen most clearly in the fact that, according to the laws of operant conditioning, positive reinforcers lose their effectiveness if they're given every single time a dog does what is desired of him; the more predictable the reinforcer, the less reliable the behavior. Yet detection dogs only work well when they are always rewarded with a toy, every single time they find drugs or explosives, etc. The reason for this disparity is that when a dog is trained through the prey drive, the training activates an instinctive, automatic sequence that has to be completed in order for the dog to feel satisfied. That sequence is: search, eye-stalk, chase, grab-bite, and kill bite. So when a dog searches and finds drugs or explosives, he feels he hasn't finished his job unless he can bite something. This is the primary reason he's always given the toy. It's not really a positive reinforcer. If it were it would reduce the reliability of the behavior overall. It's a means of completing the predatory sequence for the dog.
Punishments
"Positive punishment" is probably the consequence that is least used by modern dog trainers, as it must be used very carefully. A dog is generally only given this type of punishment if it is willfully disobeying the owner. Punishing a dog who does not understand what is being asked of him is not only unfair to the dog, but can make the dog a fearful or unwilling worker.
Punishments are administered only as appropriate for the dog's personality, age, and experience. A sharp No works for many dogs, but some dogs even show signs of fear or anxiety with harsh verbal corrections. On the other hand, certain dogs with 'harder' temperaments may ignore a verbal reprimand, and may work best if the reprimand is coupled with a physical punishment such as a quick tug on a training collar. Trainers generally advise keeping hand contact with the dog to positive interactions; if hands are used to threaten or hurt, some dogs may begin to behave defensively when stroked or handled.
Avoiding punishment
Keeping a puppy on a leash in challenging situations or in his crate or pen when not closely supervised prevents the puppy from getting into situations that might otherwise invite an owner's harsh reaction (such as chewing up a favorite pair of shoes).
Next: Dog Training part V- The command voice