The underworld is hidden in the earth. It is the kingdom of the dead and ruled over by Hades. Hades is a greedy god who is greatly concerned with increasing his subjects. Those whose calling increase the number of dead are seen favorably. The Erinnyes are welcomed guests. He is exceedingly disinclined to allow any of his subjects leave.
For most, life in the underworld is not particularly unpleasent. It is rather like a miserable dream, full of shadows, without sunlight or hope. A joyless place where the dead slowly fade into nothingness.
Geographically, the underworld is surrounded by a series of rivers: The Acheron (river of woe), The Cocytus (river of lamentation), The Phlegethon (river of fire), The Styx (river of unbreakable oath by which the gods swear), and The Lethe (river of forgetfulness). Once across the rivers an adamantine gate, guarded by Cerberus, forms the entrance to the kingdom. Deep withen the kingdom is Hades vast palace, complete with many guests.
Upon death a soul is lead by Hermes to the entrance of the underworld and the ferry across the Acheron. There is a single ferry run by Charon to take the souls across the river. Only those who can pay the fare, with coins placed on their lips when buried, receive passage. The rest are trapped between two worlds. The souls then enter through the gates. Cerberus will allow all to enter but, none to leave. The souls then appear before a panel of three judges, Rhadamanthus, Minos, and Aeacus, who pass sentence. The very good go to the Elysian Fields. Others are singled out for special treatment. Sisyphus and Tantalus being prime examples of the later.