There are four nations within Gamindustri: Planeptune, Lastation, Lowee, and Leanbox. In each nation, you can use the Shop or the Guild, both of which allow you to accept quests, as well as gather information from the various residents of Gamindustri.
Within dungeons are Event Points. Events will trigger once you reach one. Certain events contain solely dialogue, while others lead directly into boss battles. Also within dungeons are treasure boxes which let you obtain various items, as well as roaming monsters that will block the path of Neptune and her friends.
You battle with a 4-person party, and battles are turn-based, with turns coming around per unit. When it's your turn, you can control your character and move around freely on the battlefield.