Walkthrough: The Battle Tree, located within Poni Gauntlet, is just another installment of what originally was the Battle Tower. The Johto Region, Hoenn Region and Sinnoh Region all had access to the Battle Tower; the Unova Region had a similar facility with the Battle Subway; the Kalos Region introduced the Battle Maison, the exact same concept but with a different name and appearance; and now The Alola Region has the Battle Tree, that exact same in all terms, except for its given twist of featuring famous characters from previous games.
The Battle Tree has three separate modes: Singles, Doubles and Multi Battles. Singles Battles allow a player to enter up to three different Pokemon (ones that aren't banned), Double Battles allow a player to enter up to four different Pokemon, and Multi Battles allow a player to select two Pokemon and team with another (through a new feature called Scouting). The more successful you are at these battling modes, the more Battle Points you will earn. And, in turn, you can use these Battle Points to buy certain items, including Mega Stones. And the more successful you are at these competition, and if you can get a streak of wins, you'll earn even more items depending on how many wins that is.
As you first approach the Battle Tree, you will be greeted by two familiar trainers to the Pokemon Franchise. These are the Battle Legends of the Battle Tree: Red and Blue.