To start off, this game is not like any of the previous Pokémon titles. Instead it has a turn-based strategy element to it. This means that each floor of a Dungeon has an invisible grid to it (which you can make visible by the push of a button). This grid is divided up by squares. Your Pokémon will fit inside one of these squares and can move from square to square. Other Pokémon on this grid can move around as well. Think of it as a chessboard and Pokémon are your pieces.
This game does not have Trainers like in previous games, instead it has missions submitted by other Pokémon for your Rescue Team to embark upon. Missions can be found in your mailbox outside your base, on the Bulletin Board outside of the Pelipper Post Office, or by entering a Wonder Mail Code at the title screen. When your Pokémon accept a mission from one of these locations it will then appear in their Job list. The Rescue Team may not embark on these missions until you bring up your Job List menu and choose to "Accept" missions. Multiple missions can be accomplished all at once, under the circumstances that two rescue missions are not on the same floor and two recruit missions are not in the same dungeon.
Rescue Teams are made up of 1-4 Pokémon and a maximum body size of 6. The larger a Pokémon is, the more Body Size it takes up. Your starter and partner should ideally stay at a body size of 1. When you are on a rescue mission you may only recruit Pokémon who fit into your party.
To recruit a Pokémon you need to take a few things into account. First is their Friend Area, if you do not have that your chance of recruiting is already 0% unless the Friend Area comes with the Pokémon. Then it is the Recruit Rate of that Pokémon plus any bonus recruit percentage (your level bonus or the Friend Bow).