The newest incarnation of the Battle Tower, Battle Tree is unlocked by traversing Poni Island after defeating the Elite Four and becoming 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!
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 of the guide will explain what makes the Battle Tree so different (and much more difficult) than the main portion of the game, the prizes you can get (which includes the elusive Mega Stones), and some tips and tricks and reliable Pokemon to use to get you as far as you need to go.