"Human foes he did not fear, nor any death by steel or fire. But this was a black land of sorcery and nameless horror. Set the Old Serpent, men said, banished long ago from the Hyborian races, yet lurked in the shadows of the cryptic temples, and awful and mysterious were the deeds done in the nighted shrines." -- Robert E. Howard: "The Hour of the Dragon"
A southern kingdom bounded by the Western Ocean on the west, the River Styx on the north and east, the kingdoms of Kush, Darfar, and Keshan on the South. The terrain of Stygia is not well described in the Saga. There are forests, marshes, and numerous islands along the western coast; but inland the land seems mostly to have been a featureless desert, dotted with tombs and sinister ruins. In the south-central grasslands were the ghost-haunted Swamps of the Purple Lotus. The jungle rainforest began near the frontier with Darfar and Keshan. There were more grasslands and a portion of the Southern Desert at the frontier with Kush. Cultivated lands lay along the great river.
The Stygians were a mysterious people, the ruling elite tall, dusky, hawk-nosed, and haughty while the lower classes were a mixture of Negroid, Stygian, Shemite, and Hyborian stock. Stygia was a decadent nation and its total population must have been very small. Certainly arable land was in short supply, apparently being found only along the Styx. (If the presumed wetter climate of the Hyborian Age held true, Stygia should not have been a vast desert. Maybe the Stygians themselves had something to do with the devastation of the landscape.)
The economy during Conan's time may have included nomadic herding, fishing, manufacturing of jewelry such as amulets and talismans, and the production of drugs. Stygia had a distinct superfluity of sorcerers. It trafficked as far as Khitai to obtain magical nostrums. Caravan routes criss-crossed the country, bringing goods into the Black Kingdoms and raw materials and slaves out of them. Stygian silk industry and steel-arms productions are mentioned in the Saga.
Stygia was a theocracy controlled by the priests of Set, the Serpent-God. The administrative capital and seat of the king was Luxur, lying inland and south of the Styx on an important caravan route. We may presume that when the climate was wetter, the River Bakhr was navigable up to Luxur. In Conan's time it was not. The greatest port and religious center was at Khemi, on the estuary of the Styx. Sukhmet and Kheshatta were apparently caravan cities that serviced traders from the black nations. From the coast, it was possible to take a caravan trail all the way to Sukhmet and presumably beyond.
After the Cataclysm, the land of Stygia was invaded by a large body of Lemurian survivors, originally from the Far East. They destroyed a pre-human race of serpent-folk to establish what was probably the first of the post-Cataclysmic kingdoms of the West -- Old Stygia. A remnant of the serpent-race survived in the Far South and in a few other places. The serpent-worship characterizing the religion of the nation had its basis in the veneration of the vanished snake-beings.
At its greatest extent, the Old Stygian Empire embraced the lands of Shem, western Koth, Ophir, and Corinthia, as well as part of the Eastern Desert. Acheron may have taken over the northern satellites just prior to the Hyborian invasions. Stygians were driven out of Shem by Hyborian-Kothic invaders.
During Conan's time the nation represented an undefined menace of ancient sorcery. After the Age of Conan, the dominion of Aquilonia was extended as far as Stygia, whose king sent tribute to Tarantia at least once. When Aquilonia faded Shem had a go at trying to conquer the mysterious land south of the Styx. It failed; but not long afterward, Hyrkanian hordes rampaged through Stygia and into the kingdoms to the south. Thus Stygia faded away amid the chaos that preceded the advance of the glaciers.
References: Hyborian Age I-II, Tower of the Elephant, Hall of the Dead, Queen of the Black Coast, A Witch Shall Be Born, Conan the Buccaneer, Conan and the Treasure of Python, Hour of the Dragon, et al.