Basically it depends on what what sort of attacks you want you future Dragonite to use.
If you plan to use only Physical damage moves, you'll want a nature that'll boost your Attack stat, but not weaken your Speed Stat, preferability a nature that weakens your Special Attack stat, which you wouldn't be using anyway. So your best choice if this is the way you plan to go as Adamant (boost to Attack, weakens Special attack).
On the other hand, you choose to use only Special damage moves, you'll want a nature that'll boost your Special Attack stat, but not weaken your Speed stat preferability a nature that weakens your Attack stat. (Modest, boost to special attack, weakens attack)
Or if you want your Dragonite to be faster than the average Dragonite, your can choose a nature that'll boost your speed. Again depending on what moves you'll be planning to use choose the nature that'll weaken the stat you'll use/need least. (Either Timid which boosts Speed but weakens Attack, or Jolly which boosts Speed but weakens Special Attack)
Thats pretty basic stuff. I'm sure that at least one battler will disagree with something above, but if you know little you have two choices, use your head or use the ideas/standard builds people who know about it use.
If its for an ingame team (not going to battle other people) however you need not bother too much about nature.
Hope it helps, bear in mind I know little compared to the vast majority of those out there.
Edit: Btw, i'm pretty sure this would be better in the Pokémon Strategies & Movesets section.