The general flow of the game is pretty static once you manage to get past the prologues for either protagonist you choose in the beginning. The base of operations is the school, where you can do many things, like view some scenes, start requests (sidequests), fuse new Personas or shop for new weapons or armor. You can return here anytime through the use of an item (Goho-M) or by exiting a dungeon/labyrinth via the first floor.
When you're in the school doing any of the above, then you will be exploring the dungeons in the game. Each dungeon is comprised of a few floors, with one dungeon having three floors and another having as many as nine (the average is 4, though). There will be puzzles, traps and many enemies in the dungeons and the goal of each one is to get to the bottom and defeat the boss. After clearing a dungeon, you go back to the school and usually, you will see a few cutscenes before the next dungeon is unlocked.