Pokémon Mystery Dungeon's gameplay is quite different from that of the core games such as Pokémon Ruby and Sapphire. Mystery Dungeon is a Roguelike, meaning it centers around strategic free exploration of dungeon environments with a limited overworld, rather than focussing on overworld exploration with the turn-based combat common to Japanese-style RPGs.
Being a Roguelike all floors are generated at random, so the most precise directions this walkthrough can provide is which floor a particular character or item is found on. In the case of rescue missions that are not part of the main storyline even these details are randomised. In both cases the in-game rescue record describes your current objectives and what floor to find them on. Unlike many Roguelikes you cannot return to higher floors so the only way to leave is to complete all the floors, complete an objective, or use an Escape Orb.
As you progress through the main story of the game random missions will become available. These are good to go on to increase your rank, level, or just to gain some items and new friends. When you go back to a dungeon that has already been beaten almost all of the levels should be the same (what Pokémon are encountered, their level, possible items, number of floors). If information is ever needed on a dungeon for a return trip just go to that page of the walkthrough and ignore the boss and story sections. The final floor that is a boss battle or story event tends to be an empty dead end.