The next day, you will automatically go to school and witness the volleyball rally, then it's time to find the people that were slaves in the castle. The first person you need to search is someone from your homeroom, which is on the second floor. To help with this, the game unlocks quick travel by using the R1 button, allowing you to teleport around the school. Go to the second floor and into your class to the north, talking to the kid at the front, answering with anything.
In the hallway, it doesn't matter what you pick, as you and Ryuji will split up now. Your next target is a third-year student, who is on the first floor and talking with another student nearby Ann and Shiho in the long hallway on the western side. Talk to them, then there will be some texts from Ryuji, who mentions a first-year up on the third floor (also, there's a tutorial about your phone's messages and how you can only have the most recent 50 available to read). Teleport to the third floor and the volleyball player will be right around the corner.
It appears you got nothing out of him, but he did give up a nice lead that you can go on after speaking with Ryuji again. Tell him about Mishima, who you will confront shortly after, where you learn some crappy stuff. Evening rolls around and you return to your room at Leblanc, where you should just go to bed, since there's nothing else to do.
It's a new day, meaning it's a fresh start to find someone who will squeal about Kamoshida. After a short scene with Ann and Shiho, you'll run into the latter, then talk with Ryuji after that little run-in. When he asks you what to do with Kamoshida, answer with both questions to get a third option, which triggers the appearance of Morgana...in actual cat form. You relocate to a better spot, where you hear Morgana's master plan, which has one little flaw to it.
While you think about that flaw, you'll be heading home when you see Ann at Station Square after riding the train near your school. She'll run off and you decide to give chase, so follow her down the stairs to the Underground Walkway. Go down the stairs next to the escalator, turn west (on your map) and look for Ann next to a green pillar. Talk with her there to initiate some scenes, where you learn of her problems. After some more scenes, you'll return home, where you'll get a text from Ryuji. Go to bed after that and get ready for the next day.
Some scenes will happen at the beginning of this and when they are done, you need to get to the courtyard. Start by going downstairs and there's a horizontal hallway to the north on the first floor, but it's impossible to get through because of the crowd. Ryuji suggests going through the Practice Building, which is to the south and then east. Once you arrive there, go north and then west to get to the courtyard. You learn about some things and Ryuji goes running off after Kamoshida. Go to the second floor and chase after Ryuji as he goes into the PE Faculty Office.
Well, you certainly see the true colors of Kamoshida, but you have something up on him that he doesn't know about, the other world. When everything is said and done, enter the castle via the hole on the western side, and get close to the entrance hall. Since going that way will be impossible, enter the door to the west to run into a guard right there. You'll be forced into a battle, where you'll learn a new mechanic, Shadow Negotiation.
In order to talk with the Shadows, you need to initiate a Hold-Up, which you do by attacking them with their weakness. As always, it's better to learn from actually doing it, so attack the Beguiling Girl with your gun to knock her down. Choose any of the options twice to get Pixie to join you as a new Persona. Before you can figure out what's going on, you're attacked by another guard, consisting of two Bicorns. Before moving on, it's time for a little tutorial.
Note: From hereon out, the actual names of the Shadows will be listed instead of their in-game names, unless they don't have one.
It's time to take a little break from the main story to quickly talk about Personas. The main character in the game has the potential to use multiple Personas and you can gain new ones through Shadow Negotiation (for right now). Whenever you knock them all down in a battle, you initiate a Hold-Up, as you already know. Press the X button during this to talk to the Shadows, where you can either ask them for money, items or for them to lend them your power.
Obviously, the last choice is what you want to go with in order to get them into your party. However, this is where things get a little complicated, as you need to know how to respond to their questions. Every Shadow that you can recruit has a personality attached to them. Luckily, there's only four of them, so you don't need to delve too deep into things. You can find out the personality of a Shadow by analyzing them and looking in the top left corner.
The four personalities are Gloomy, Irritable, Timid and Upbeat. Each of these have their own responses that are liked or disliked, which also fall into four types: Ambiguous, Kind, Playful and Serious. Once you choose "Lend me your power," you have to answer two questions and depending on the above criteria, they can either join you, give you an item or attack. They will usually only leave an item if you already have that Persona in your possession or that particular Shadow is a higher level than your character. There is one slight problem with the whole recruiting thing, though, which is that the responses aren't labeled, so you need to take a guess sometimes.
Note: If you have had the Persona in your possession at one time, but not anymore, then you get an additional option. The top option goes through the normal recruiting process, while the bottom one will make it so that Persona will join you without having to do all that again.
Back to the Action
Alright, that little distraction is over with, so you should be in the middle of a fight with two Bicorns. At the beginning, you'll be forced to switch your Personas by pressing Triangle and then L1 or R1 to get over to Pixie and choose her. This is very convenient, too, as the Bicorns are weak to electricity and Pixie just so happens to have the Zio skill. Use this on each of them to knock them down, then do whatever you want during the Hold-Up, though it might be helpful to try and recruit one to help build your library of Personas.
Whatever you do, exit that room through the other door and head all the way north to another, noting the iron bars blocking the passage in the middle. You should now appear in a larger room that has three enemies roaming about. Use the pillars to get ambushes on them and if you can, try to recruit any new Personas by exploiting their weaknesses (look at the chart below for weaknesses). Also, if you run into any repeat Personas, it might be a good idea to extort them for some money, as that is a relatively scarce resource right now.
Tip: To make things a little easier in a bit, it's a good idea to try and get Jack-o-Lantern as a Persona, as he is the only one right now that has access to a fire skill (Agi).
If you explore the room a little bit more, you will find a chest in the southwest corner, which contains a Silver Dagger , an upgrade for the main character. Continue through the northwestern door and you'll come upon another Safe Room. You'll discuss some strategies, when you overhear something that turns out to make things go very bad.
Well, it turns out that Ann somehow found her way back to the castle and got taken by the guards, so you need to go rescue her. Unfortunately, you can't go any deeper into the Palace, so go back the way you came to find those bars are now gone. Welp, things go a little wrong for the pervy teacher, as Ann awakens to her Persona and there will be a "mini-boss" here. The Guard Captain is weak to fire, which Ann's Persona, Carmen, just so happens to have. Use this to knock him down, then initiate an All-Out Attack to deal some big damage.
If you have Jack-o-Lantern, then do the same thing, but opt out of the Hold-Up and change your Persona. The reason for this is that Jack-o-Lantern is weak to wind and the Guard Captain has Magaru, a wind attack that hits your entire party. It is also a good idea to guard with Ryuji, for the same reason, as you don't want the Guard Captain to get another chance to attack. You should be able to finish the battle on the second round if you follow the above strategy.
Your party will leave the dungeon after the battle and back in the real world, you'll end up starting the Lovers Confidant with Ann Takamaki. At Rank 1, you get the Baton Pass ability, which allows you to pass your turn over to someone else with Baton Pass after a One More. You also get a new hideout, which is just the roof of your school. At Leblanc's, feel free to talk to the woman sitting down, then head up to your room. Upstairs, you'll end up getting another Confidant, Morgana (Magician). At Rank 1, you get Infiltration Tools, which you'll see about in a few in-game days. For now, go to sleep to continue to the next day.