As your second day in The Alola Region comes to a close, you will receive another knock on your door. As you go to answer it, Professor Kukui will once again let himself in. From there, he will escort you to the Festival in honor of Tapu Koko in the Trial Area.
As he does, Kukui will first show you how to catch Pokemon, ending by giving you a number of Poke Balls for you to try it out on your own. He will then leave you to search for Wild Pokemon and Battle the numerous trainers on Route 1. Since this path is pretty short, there aren't too many trainers and different species of Pokemon standing in your way to the Trial Area.
Once you arrive at th Trial Area, the Festival quickly begins with you facing off with Hau, your Rival, once more. He has trained his Starter Pokemon some, as well as adding a Pichu into his arsenal. Again, he should an easy defeat.
After defeating Hau, the grandson of Hala, Kahuna Hala himself will give you the Z-Ring, something he made out of the Sparkling Stone you gave him, a trait only a Kahuna has. Unfortunately, you do not yet have any Z-Items that will allow you to use a Z-Move on your Pokemon at this stage in the game. After giving you this, the Festival quickly ends and you character goes home. Once home, you will have a quick chat with your mother before the game cuts to the next morning.
Once it's morning, there is again another knock at the door. Your mother believes it will be Kukui again letting himself in, but you still must go and answer it. Instead of Kukui, it is actually Lillie who has come to take you to Kukui at his Research Lab just south of the house you live in. Follow Lillie, through the number of trainers and wild Grasses, and you will quickly get to Kukui. He is training with his Rockruff as you arrive at the gym with Lillie.
After going into the Research Lab, Kukui will quickly update your Pokedex into the Rotom Pokedex. This Pokedex also comes with a map that shows exactly where your player needs to go. Hau soon arrives, and after he does, Kukui asks if you two are going to take the Island Challenge, the storyline that has replaced the usual Gym Leader ones for The Alola Region. In this system, the Gyms have been replaced with Trials and Grand Trials. Trials are given tasks you must perform, differing from one to the next, finishing by defeating a super strong Pokemon known as a Totem Pokemon. The Grand Trials are all battles with the Kahuna on the given Island.
Both you and Hau will quickly accept the challenge, just before Lillie offers to escort you to the area to the west of your house, the path that was earlier blocked by Tauros. Follow her, and you will quickly find yourself at the Trainer's School. Once there, you will be challenged to find and defeat four trainers before leaving. After accepting, Kukui will give you the Exp Share Key Item that allows for all party Pokemon to received Exp from battles, whether involved or not.
Find and defeat the four trainers, and then you will take on the teacher in a Battle. Defeat her too, and the challenge is won. After such, Kukui will introduce you to Captain llima, the trainer who runs the first and only Trial on Melemele Island. After this, Lillie and Hau will both escort you to Hau'oli City, the largest city in all of Alola. Follow them and your Rotom Pokedex, because this is truly when both your adventure and the storyline will begin to develop.