Examples of a caffine hangover include:
Being Ratty with everyone and everything
Caffeine, like alcohol, is a diuretic (a substance that makes you pee a lot), and much of the "hangover" symptoms -- nausea, vomiting, headache, dizziness, etc. -- are a result of being dehydrated.
The best way to avoid getting a caffeine (or alcohol) hangover is to not only limit your intake of caffeine or alcohol, but to also drink plenty of water, or better yet sports drinks like Powerade or Propel, to keep yourself hydrated while you party. You may look like a dork doing it, but you'll fare a lot better than your friends will in the morning.
Sports drinks are also the best and quickest hangover cure because they not only hydrate you, but replenish your electrolyte balance as well.