After you explore the big city of Mesagoza, you enter the Academy for your first day of school. In Scarlet, you attend Naranja Academy, and in Violet, you attend Uva Academy.
Explore the Academy
After some cutscenes, you can talk to your fellow classmates, then exit the room. You have a couple of destinations to choose from.
If you go to the Cafeteria, you can buy a meal, and talk to Arven. You will learn about the Herba Mystica, and the Titans that guard them. Arven will mark the locations of the Titans in your Map App. He will give you a Bag of Stardust.
As you leave the Cafeteria, you get a mysterious phone call on your Rotom Phone from Cassiopeia, who asks you to help with Operation Starfall, a plan to defeat Team Star.
Afterward, you will be in the entrance hall. If you already talked to Nemona in the Staff Room, there will be an announcement telling you to go to the Director's Office. You can use the computer next to the front desk to go there, or to the Staff Room if you haven't talked to Nemona there yet. Or if you want to explore the Academy before you continue, you can stay in the entrance hall.
You can talk to the person behind the front desk in the entrance hall of the Academy to take classes. When you take a class, there will be a cutscene where you learn about various things that you can do in the game. More classes will be unlocked as you progress through the game.
There are many books in the entrance hall of the Academy, including (in Scarlet) the mysterious Scarlet Book, or (in Violet) the mysterious Violet Book, which will tell you more about the mysteries of the Great Crater.
If you go to the Staff Room, you'll see Nemona talking to a trainer called La Primera, and Nemona will tell you about reaching Champion Rank. You have to win at the eight Pokémon Gyms and get their Gym Badges, then take the Champion Assessment. She also mentions the Treasure Hunt, which is an independent study program outside of the Academy, an adventure where you can learn however you want. Nemona marks the locations of the Gyms in your Map App.
Afterward, if you already talked to Arven in the Cafeteria, there will be an announcement telling you to go to the Director's Office. When you try to leave the room, you can choose the Director's Office, or choose the Cafeteria if you haven't talked to Arven there yet.
At the Director's Office, you meet the Pokémon Professor (Sada in Scarlet, Turo in Violet). The professor asks you to look after the mysterious Pokémon that you found on the beach.
Afterward, as you leave the room, Nemona arrives to show you to your dorm room.
Your Dorm Room
After the cutscene, you won't be able to leave the room until you rest, so check on the bed to rest.
After that, go to the door of your dorm room. You have to choose Schoolyard, so do that.
The picnic feature is now unlocked in the menu, and you have received various new picnic items in the picnic section of your bag. You can only have picnics outside on level ground.
More to Explore in the Academy
Once the Treasure Hunt begins, you can use the computers in the entrance hall of the Academy to go to more places, such as the School Store, Biology Lab, Art Room, and so on. The School Store sells many supplies that are helpful in battle and in the field, such as different types of Poké Balls and a wide variety of healing items.
Get to Know Your Teachers
When you check the computers in the Academy, you may sometimes see an exclamation mark next to a room name, and a picture of someone on the map to the right of the room names. If you go there and talk to that person, you will learn more about that person, and in some cases you will unlock more features of the game or receive rewards.
Meet up with Nemona
When you're ready, go outside and go south from the Academy building to find Nemona. There will be a cutscene. During the cutscene, Cassiopeia calls and tells you more about Operation Starfall. Team Star has five crews, each with their own base. Cassiopeia marks their locations in your Map App and will send you rewards each time you defeat one of Team Star's crews.
Ride on Koraidon or Miraidon
You can now press the + button to hop onto Koraidon or Miraidon. While on your Pokémon's back, you can press B to jump, or press + again to get off of your Pokémon and walk around again. Press + now to proceed.
More classes are unlocked at this point. You can go back to the entrance hall of the Academy and talk to the person behind the front desk whenever you want to take the classes.
At this point, Mass Outbreaks will start to occur. You can check your map to look for Pokémon icons on the map, or question mark icons if there is a Mass Outbreak of Pokémon that aren't in your Pokédex yet. At a Mass Outbreak, the more Pokémon that you defeat in the outbreak, the more likely you are to encounter a shiny Pokémon of that type (i.e. a Pokémon with a different appearance from usual).
You can now participate in Tera Raids. They are indicated by star-shaped symbols on the map, which change each day at midnight on your Nintendo Switch. If you go to one of those symbols on the map, you will find a glowing crystal. If you check on the crystal, you will be shown the silhouette of the Pokémon that you can battle at that location. This Pokémon will be Terastallized, and its type is indicated by the symbol above the Pokémon's silhouette. You can choose which of your Pokémon to send against it, and you can either battle alone with NPCs, or you can battle alongside a group online.
You can optionally go north from the Pokémon Center in western Mesagoza to find the cave leading to the Pokémon League. You won't be able to enter the Pokémon League building until you have won all eight Gym Badges, but you can catch Pokémon in this area, and you can battle Jaxon the Student, who has a level 14 Meowth. You get 616 Pokédollars for winning.
There is another trainer farther north, but this trainer's Pokémon are all level 56, so make sure not to talk to this trainer until you have progressed further in the game.
You can use the Pokémon Center here to add it as a Flying Taxi destination.
There is a Gimmighoul on top of the Pokémon Center here, and also on top of the Pokémon League building itself, but you can't reach them right now. There is another Gimmighoul around the west side of the Pokémon League building, and there is a TM132 Baton Pass behind the building.
You can go back into Inlet Grotto with Koraidon/Miraidon to find a TM151 Phantom Force on top of a column of rock.
You are now free to go on an adventure at your own pace. You can search for the Titans that Arven mentioned, and you can challenge the Pokémon Gyms that Nemona mentioned, or you can just explore Paldea and discover things along the way.
Many destinations have been added to your map. The destinations will be labeled with "Victory Road" if they help you get Gym Badges or lead you toward attaining Champion Rank, "Path of Legends" if they lead you to Titans and the Herba Mystica, and "★ Starfall Street ★" if they lead you to the bases of Team Star's crews.