Bassically, the fight starts when Jake's Toruk grabs a scorpion gunship and throws it at the side of one of the floatin' mountains.
At the very start of it all, even before the movie: the Na'vi see these metal machines descending from the sky, and the small, in comparison to the Na'vi, humans emerge from the machines. Now I haven't read anything that makes me belive this, but this how I think it started. I believe either the Na'vi first attacked the humans out of fear and thought to be defending themselves, and then the humans responded with force; or the humans attacked many predatory animals to keep themselves safe, and the Na'vi disapproved, attacking the humans.
Also, it could have first been a misunderstanding, both sides attacking the other in what they thought was defense, and what now has turned into never-ending conflict. ---^^untrue...humans first discovered the planet then landed and attempted to coerce the navi by building schools and teaching them english. but they were happier with their orginal lifestyle and began to run the humans off.