What do I do to tell my puppy that biting is wrong?

Just a light tap or flick on the nose tends to teach them. Nothing that can hurt them, but enough for them notice that you're in charge, you're the leader. I heard it on the Dog Whisperer :D, it deffo works though i had the same thing, i just tap them on the nose and say "no" in a negative tone. seems to work, then play when they've calmed down a bit :)