The most important building in Pokemon Sun and Moon are Pokemon Centers. They are one stop shops for all your Pokemon needs, and can be found in every major city.
Speak to the nurse behind the main counter to heal your entire party completely for free. Their HP, PP, and status condition will all be restored.
Use the PC at the main counter to access the Pokemon Storage System. You can deposit or withdraw any Pokemon you have captured on your adventure. If your party is full, the next Pokemon you capture will automatically be sent to the PC, or it can be switched with another Pokemon in your party. Up to 900 Pokemon can be stored in the Pokemon Storage System (30 per box).
If a special event Pokemon is being distributed, you will receive it from a delivery man in a Pokemon Center after accepting it through the Mystery Gift option at the main menu of the Pokemon game.
There is also a Poke Mart counter on the right side of every Pokemon Center. They sell various items specifically for Pokemon. It’s best to pick up healing items to make you adventure go smoothly. The more badges you earn, the more items they will have in stock. Stat-enhancing items can also be found at certain shopping centers in game to buff up your team, though these items are pretty expensive.
The counter on the left side of the Pokemon Center is the Pokemon Cafe. Speak to the merchant here to receive Poke Beans to feed your Pokemon in Pokemon Refresh, and buy drinks once a day. Each Pokemon Cafe carries different items.