The newest incarnation of the Battle Tower, the Battle Tree is unlocked by traversing Poni Island after defeating the Elite Four and becoming the Champion of Alola. Enter Poni Grove, previously blocked by an NPC, and traverse Poni Plains and Poni Gauntlet.
Once you reach the area, you will be challenged by Red and Blue. Pick which one you want to engage in a standard Pokemon battle, and after you win, you unlock the Battle Tree! Sorry, but you can’t fight them both (you could always soft reset if you can’t choose).
The Battle Tree is pretty special. You’re going to need more than just brute force to win. You will need strategy, properly trained Pokemon, and a little bit of luck to get a win streak going and keep it that way. This section will hopefully provide you the instruction and insights you need to start your Battle Tree streak.