After the initial cutscenes, you'll be able to enter a name for your character. Note that it goes last name, then first name. After that, you're introduced to two characters living in the dorm and you'll be shown to your room. Once morning arrives, you'll be escorted to your high school by Yukari. After talking to her a little bit in the lobby, you will be free to move your character around.
You can check the bulletin board to see which class you're in, but your goal right now is to get to the Faculty Office. Head through the opening opposite the bulletin board to appear in a hallway, then enter the Faculty Office. After meeting your homeroom teacher, you'll have to sit through the opening ceremony. After school is over, you'll meet Junpei Iori, and after some friendly banter with Yukari and him, you walk home with Junpei.
Back at the dorm, you can save your game at the sign-in sheet on the counter (remember to save often). You can have a look around the dorm if you want, but there's not a lot to see. After your little sightseeing tour of the dorm, head over to your room on the 2nd floor by either going there on foot or choosing the option when accessing the sign-in sheet. After a short cutscene, you will move onto the next day...