Short answers, pulled from the story.
The Titanomachy was a ten-year war fought in ancient Thessaly between the Titans, the older generation of gods based on Mount Othrys, and the Olympians, who would come to reign on Mount Olympus. The war ended with an Olympian victory, allowing Zeus, Poseidon, and Hades to divide dominion over the sky, sea, and Underworld respectively.
The Titanomachy grew from a cycle of usurpation. Cronus overthrew his father Uranus, who warned that Cronus's own children would one day do the same. When Cronus began swallowing each child born from his wife Rhea to forestall the prophecy, Rhea hid their youngest, Zeus, who eventually freed his siblings and launched the war.
The Cyclopes forged thunderbolts for Zeus, a trident for Poseidon, and a helmet of darkness for Hades. They were freed from Tartarus by Zeus, who slew their guardian, the she-monster Campe, before the war began in earnest.
Atlas, who served as second in command of the Titan forces after Cronus, received a unique sentence: he was not imprisoned in Tartarus like the other defeated Titans, but was condemned to hold up the vault of the sky permanently.
Styx was the first deity to ally with Zeus, arriving with her four children: Nike, Zelus, Kratos, and Bia. Zeus rewarded her by naming her the great oath of the gods.
A now-lost poem also titled Titanomachy, distinct from Hesiod's Theogony, was traditionally attributed to Eumelus of Corinth, a semi-legendary 8th-century BC poet. The poem was divided into two books and opened with its own theogony before the battle narrative. Many ancient authors cited it without naming its author; the name of Eumelus was attached because it was the only name available.