After you meet the Island Kahuna, Hala, you go to Iki Town to participate in the festival.
Learn How to Catch Pokémon
Go outside and follow Professor Kukui to Route 1. He will show you how to catch wild pokémon. You don't have to press any buttons during his pokémon battle. Afterward, he will give you 10 Pokéballs and 5 Potions. You can go back home and talk to Mom to heal up your pokémon.
Pikipek, Caterpie, Metapod (near Iki Town only), Grubbin (near Iki Town only), Pichu (near Iki Town only - rare), Yungoos (day only), Ledyba (day only), Rattata (night only), Spinarak (night only)
Go through Route 1, catching pokémon as you go. Be sure to get the Potion that is next to a rock near the fence.
After that, a pokémon trainer will be in the path and you will have to battle him. He is Youngster Jimmy, and he has a level 3 Rattata. You get 60 Pokédollars for winning.
Up ahead, you can go behind the pokémon trainer to get a Poké Ball from next to a palm tree.
Then you can battle the girl. She is Lass Audrey, and she has a level 3 Caterpie. You get 72 Pokédollars for winning.
Before you go northwest, there is an Antidote south of a fence after Lass Audrey.
If you try to go southeast, a kid will tell you to go to the festival. The festival is northwest, but you can go southeast to go back to your house if you want to.
Go northwest from the crossroads to find a Potion. If you keep going west, you find a trainer. It's Preschooler Oliver, who has a level 4 Yungoos. You get 48 Pokédollars for winning.
Go west from the trainer and you can get a Paralyze Heal to the left of the stairs.
Iki Town Festival
Go up the stairs to enter Iki Town. Kahuna Hala will talk to you about the festival.
Go north and you find Hau and his pokémon. Kahuna Hala heals your pokémon, then asks if you are ready to battle. If you say no, you can talk to Kahuna Hala when you are ready.
You battle Hau, who has a level 6 Pichu (weak to Ground attacks) and a level 7 Rowlet (if you chose Litten), Litten (if you chose Popplio), or Popplio (if you chose Rowlet). You get 140 Pokédollars for winning.
After the battle, Kahuna Hala gives you the Z-Ring. Then after a cut scene, you go back home and rest for the night.