When you regain control, you will be in the subway just outside of your school, so exit to reach it and go inside. You'll now be in class with Mr. Ushimaru, where you'll be asked a question. The correct answer is "Logic," which will increase your Knowledge a little bit. Knowledge is one of five Social Stats in the game, which affect your everyday life. They will be used for checks during some cutscenes, determining whether you can do something or not, as well as requirements for starting/leveling certain Confidants (you'll see this soon).
Once class is over with, some scenes will play out and you'll eventually return to the mysterious castle. Morgana meets up with you again and you'll head back inside, so follow him into the entrance hall. Go down the stairs and through the doorway to find one of those armored guards you saw the last time. Morgana will teach you about how to encounter enemies in the field. When you get close enough, press the X button to strike the enemy and if you connect, you will start a battle.
Note: If the enemy hits you before you attack, then they will get the first turn. If you approach them from behind without being noticed, the Ambush icon will appear, which gives you a pre-emptive.
Test it out on the guard ahead of you to feel it out, then continue in that direction to pass by the cells from earlier, which have no one in them. Due to some guards likely coming, your party ducks into a side room, where you learn about Safe Rooms. These rooms are basically areas where you don't have to worry about enemies and can even save your game, as well as other uses later in the game. Ryuji also hands over a toy gun (Tkachev) and a Medicine . Exit the Safe Room to overhear a conversion from the guards about the location of the slaves.
Continue down the hallway and stairs to find another guard, where you'll learn about the Security Level. The basics of it is that if you are seen, the security level will rise and if it gets too high, then you will be booted from the Palace. Kill the guard ahead, then use the door that is marked on your map. As you go down the stairs and around the corner, there will be another short scene, then another battle where you'll be introduced to Guns.
Security Level: The Security Level will increase if you get spotted by enemies on the map, with enemies becoming more alert as it gets higher. If it gets too high, then you will be booted from the Palace. You can decrease it by ambushing enemies without being seen, plus it will naturally go down as days pass.
Guns are accessed by pressing up on the directional pad and are generally stronger than melee weapons. However, they have limited ammo and you can't regenerate ammo unless you return to the real world (there is an item you can get later, but it's not easy to come by). For now, fire one shot at the Beguiling Girl to knock it down, then attack it in any other way. You don't have the weakness for the other enemy, so just do whatever you want. After the battle is over, you will receive a few more tutorials on Party Tactics, Rush mode during battle, and Skill Selection Assistance.
The most important of the above is probably assigning tactics to your other party members. This is done by either pressing L2 during your character's turn in battle and selecting the Tactics option, or by choosing Stats on the Triangle menu outside of battle. You have Act Freely, Full Assault, Conserve SP, Heal/Support and finally, Direct Commands. With the final option, you have full control over every single move your allies will perform. It may be a good idea to set Morgana to "Direct Commands" for now, as he's your only other party member and it'll be easier to make sure he doesn't use all of his SP.
Continue on this path and when it starts going north again, be careful of the guard around the corner. When you turn the corner there, you will get into another scripted battle, where Morgana will teach you about All-Out Attacks. Using the battle as an example, hitting them with their weakness will cause them to fall down and if all of the enemies are knocked down, then you will initiate a Hold-Up. From here, press Triangle to do an All-Out Attack with your character and any other party member that isn't incapacitated.
All-Out Attacks: These powerful attacks occur if you knock down all of the enemies in a battle by exploiting their weaknesses, where you can choose to do it or not during the Hold Up. However, you cannot do them if the main character cannot act or if he's the only one who can act.
There's nothing at the nearby dead-end, so just go through the door to reach the next area, where you'll find the Training Hall...of Love? Okay. Move forward to view a scene about the students in the cells, then you'll need to check out two specific ones. They are in between the doors marked on your map and depict students running on a very fast treadmill and another getting blasted by some volleyballs.
Escape From The Castle
All right, that's all you can do here for right now, so it's time to escape from this hellish place. When you return to the previous room, you will end up running into another guard, so you'll find another way out. You'll end up back in the entrance hall, where another encounter with Shadow Kamoshida will happen. There will be another fight with three Dirty Two-horned Beasts. While you can try to do something, you can't win this battle, so just guard on your turn to quickly end it without having to worry about anything.
A lengthy scene will happen, where some things will happen, earning yourself another party member. Yep, Ryuji has awakened to his Persona and you are thrown into another battle, this time against the gold guard. While it comes across as a mini-boss, it's nothing you need to fret over. The guard captain will start by summoning two of those horned beasts from the previous battle. Luckily for you, Ryuji's Persona has Zio (electric) and these horned beasts just so happen to be weak against them.
Use Zio on each of them once, then do it one more time on another. The big guy doesn't have any weaknesses, but is strong against a few of your elements, so stick with physical attacks to make it easier. Heal when necessary (try to just use Dia so as not to waste any items) and the enemy will go down very easily. Watch the scenes that follow the battle, with you eventually exiting the castle and returning to the real world. You'll unlock your first Confidant in the game, for Ryuji and the Chariot Arcana.
Confidants: If you've played the previous two Persona games, then you may recognize the Confidants as Social Links. They are people you relate to you that you share a special bond with. They are more powerful in this game, as each one will grant you abilities as you level them up. There are two types of Confidants, those that level up automatically and those that require you to hang out with them to level up.
Eventually, you'll return home and will be in your room. If you look in the bottom left corner, you see "IM" attached to the Square button, which is the text messages on your phone. Go to your bed to see some more messages from Ryuji, then select it again to head to sleep. You'll have another "dream" with Igor, but you'll establish the Fool Confidant this time, earning two abilities from Rank 1, Wild Talk and Arcana Burst. Both may be a little foreign to you, but the former lets you negotiate with demons in battle and the latter will grant bonus experience to fused Personas of the related Arcana, based on that Confidant's rank.