After getting your starter pokémon and battling Hau, you enter Iki Town.
Professor Kukui says to go north to the ruins to introduce yourself to Tapu Koko, so go north and follow the path, and go north from the wooden platform to reach Mahalo Trail.
As you go up the trail, you will see a blonde girl. During a cutscene, a mysterious pokémon will float out of her bag onto the bridge, only to be attacked by three Spearows.
When you go up to the girl, she asks you to save her pokémon. Start crossing the bridge and you will have to battle a Spearow. After that, go across the bridge. Sometimes you will stumble, but keep going up. When you reach the pokémon, there will be a cutscene.
Back to Iki Town
The girl will introduce herself as Lillie and will give you the Sparkling Stone. Afterward, go south toward Lillie to go back to town with her. Professor Kukui introduces her as his assistant.
Kahuna Hala returns. During a cutscene, Professor Kukui will give you a Pokédex and a Trainer Passport.
If you open your menu, there are new options available. You can look at your new pokémon. You can take a look at your Trainer Passport, where you can customize your trainer portrait photo by pressing A.
You can also look at the pokédex, which has your starter pokémon in it and any other pokémon you have encountered so far.
When you try to leave the wooden platform, a cutscene will occur. Kahuna Hala will ask to see your Sparkling Stone. He will give it back to you the next day. He invites you to the festival tomorrow.
You will automatically go back home and introduce your starter pokémon to Mom. The next day, you will go to the Festival.