Mutt does a great job of explaining these for the most part, I only have 1 tiny critique (which doesn't matter TOO much for general stuff, but for anyone who wants to go further than just training their own dogs).
What determines whether something is reinforcement or punishment is the actual RESULTING behavior, not the INTENDED result.
You could squirt your dog with a hose with the intention that he/she will stop barking, however if the dog actually starts to bark MORE then you are actually REINFORCING the behavior, despite the fact that you think your dog doesn't like being squirted with the hose. And sometimes we try to do things that we think will be punishment (choke chains/prongs/etc) and the dogs just don't give a darn and the behavior doesn't change one way or another.
The easiest way I have found to determine what quadrant a stimulus falls in is by asking these questions:
What is the behavior?
Is that particular behavior increasing or decreasing?
Are you adding something in, or taking it away?
Increase = Reinforcement
Decrease = Punishment
Adding something = Positive
Taking something way = Negative
Then piece it all together.
So for my above example with the barking dog:
What is the behavior? Barking
Is the behavior increasing, or decreasing? Increasing
Are you adding something in, or taking it away? Adding something
So we have that squirting the dog with the hose is Positively Reinforcing the barking.