It's a bit weird, really -- all outer planes are somewhat coexistant.
The Earth is the Land of Mortals. The Moon, which is big, blue and green, more a twin sister planet than a satellite, is the Land of the God and the Land of the Souls. Dead people goes there (funerary ceremonies are thus always practiced at night time, and never in a new moon).
Daytime is thus the Time of Mortals, who have all their stuff to do. Nightime is the Time of Gods, who do their divine stuff -- hence, it's the time of religious ceremonies, prayers, and magic. People are less afraid of the night (notably because the big moon, much bigger than our own, shines more -- on the other hand, the new moon are scary).
The inner planes "correspond" to the Sun. People believe that the sun is made of 6 layers, and each of these layers is connected to one of the inner planes. The top layer is obviously that of the Fire, but the order of the other is disputed. The main school of thought tell it goes that way: Earth (the kernel), negative energy, water, positive energy, air, fire.
Those strange outsiders, like the Slaad or the Formians; or the Modrons and Inevitables, are linked to some of the planets. Some say one of the planets is the mirror of Earth and is the "home" of the Plane of Mirrors. There, they say, all things are reversed, and on this planet you walk on the ceiling, and other weird stuff like that. (Obviously, the people having said that have not traveled there.)
The Plane of Faerie is connected to the Earth. But, in the Nether regions, the bowels of Earth are connected to the Lower Planes. There, in the dark caves hidden from the Gaze of the Moon, archdevils and demon princes live in their demiplanes. The deeper you walk, the greater the risk you have of stepping into Hell, Abyss, or a less well known plane. (As a result, while people on the surface usually worship the deities of the Moon, the horrors that dwell below -- deep orcs, illithids, aboleths, kuo-toa, etc. -- worship fiends, who are "nearer" from them. This also explains why you don't have Gzemnid or Maanzecorian living in a lunar city nearby to some human deity, and why the deities of these foul beings aren't well-known on the surface -- hey, you may litterally spy on the gods with a telescope!)
The Ethereal, Astral, Dream, and Shadow planes reach everywhere. While Dream is a bit special (and don't truly reach anywhere, in fact), the Astral, Ethereal, and Shadow eventually merges. When you go far, far away, when you travel to the limit of the planetary system, they become Deep Astral, Dark Shadow, and Far Ethereal -- three names for the same thing. The plane that serve as interface between the World, and the Far Realms. Access to other cosmologies isn't through the Plane of Shadows, but through the Far Realms.
From the Far Realms, several horrors crept: the Illithids and their Grell allies (they're together IMC), the aquatic Koprus (distant forebears of the Illithids, and their bitter enemies), and of course the Kaorti. The Ethergaunt reached the Far Realms through the Far Ethereal, and mutated there.
A tale only the most erudite lorekeepers may say is that, in the beginning, Earth and Moon were one. Then one day, a mortal commited a crime against a god, and other gods decided to make two separate realms. But not all deities knew of what would happen. Some lesser deities, among the less liked of them (usually because of what we could call an attitude problem), were left in the black. When the sundering happened, the Earth was shattered. Whole landmass were removed, as matter was torn and used to fashion the Moon. The center of the Earth was no cosmologically empty, its metaphysical matter and energy removed to make the Moon or fill the gaps on the Earth. (This rift created the Ark of Limbos, a localized phenomenon of non-existence, which is central to the campaign.)
Back to our gods left out of the plot. As a result of the sundering, they were bereft of flesh and forced to incarnate into the very land.
(This had several effects, most notably the fact that now places have an empathy -- that's the source of that bad feeling one may get in a place where horrors have been done, the place itself recalls these horrors, and you may feel them. Several ghosts phenomenon comes from there, a weird example could be when someone the place "liked" die, it will ensnare that person's spirit to make a ghost, or create one from its memories of that person. Most places are traumatized to coma by the sundering, and are only active on an "inconscient" level. Psionics magic comes from the fact of attuning one's mind to the twisted psyche of the place's spirit, and influencing it.)
The servants spirits (outsiders like celestials, fiends, arcosopher* or anarchon*) of these deities were devoid of leader, "free" to do what they wanted. Free celestials of arcosophers rejoined deities on the Moon, or where slaughtered by the free fiends. Free anarchons mutated and wandered, becoming weird creatures or eventually changing into a "natural" creature (like dragon, lamia, human, or rabbit) and ceasing thus to exist as an outsider agent of chaos. The free fiends, however, took advantage of the void to build demiplanes. Thriving on negation and loss, they built the grim lower planes, as traps feeding on despair, corruption, and damnation.
On the surface, of course, this was the end of civilization. And below the surface, even worse. The cataclysm destroyed everything. There were few survivors indeed. A new, ravaged, world to heal and colonize. Knowledge of the World of Before was soon lost entirely. Indeed, one of the first new civilization was called "the Amnesiac Empire". Built by snakefolks, they were fanatically obsessed by the Before, why all was forgotten, why all was destroyed. Since then, that empire has disappeared, and the ophidians (not as the ones from the Fiend Folio) were driven extinct.
But, back to our fiends. They came, and proposed their help for the rebuilding. They proposed knowledge to those that seeked to retrieve magic. They proposed lots of things that were so much needed few people objected the price. And this gave them a steady supply of souls they used to forge more of their kind, or to strengthen their planes, as they started the Blood War among themselves (reduced dimensions compared to Planescape's infinities of infinities, but still impressive). Soon, the lower planes were virtually infinite. Several races of the depth were irremediably corrupted by the fiends. Only the rediscovery of the gods by the "Amnesiac Empire" saved the surface.
