How Did Paul Atreides Become Emperor?

Paul Atreides became Emperor by defeating Shaddam IV on Arrakis and forcing him off the throne. He held the spice hostage, threatening to destroy it and with it all space travel, so the Spacing Guild and the Great Houses had to deal with him. Then he married Shaddam's eldest daughter, Princess Irulan, and took the throne through her claim. (Dune)

The spice was the throne#

Everything in the Imperium runs on melange. It lengthens life, and the Guild Navigators need it to steer ships between the stars. It comes only from Arrakis. (Dune)

When Paul drinks the Water of Life and wakes as the Kwisatz Haderach, one of the first things he sees is what that means. The Guild depends completely on the spice, and whoever can destroy the spice controls it. Paul, with the Fremen, can. (Dune)

Winning the battle#

Fremen raids had choked the spice harvest, so the Emperor came down to Arrakis himself, with five legions of Sardaukar. The Guild and the Great Houses waited in orbit. (Dune)

Paul struck during a great storm. The Fremen used the old Atreides family atomics to blow a gap in the Shield Wall, the cliffs that protected Arrakeen, aiming at rock rather than people so as to stay within the rules on atomics. Then they rode sandworms through the gap. The Sardaukar, who had never lost, were overwhelmed in the Battle of Arrakeen. (Dune)

During the fighting, Paul's sister Alia, who had been captured and brought before the Emperor, killed Baron Harkonnen with a poisoned needle. Paul walked into the Emperor's audience hall as the victor. (Dune)

Taking the throne#

Military victory wasn't enough on its own. Paul faced the Emperor, his household and the Guild's agents, and threatened to destroy all the spice on Arrakis unless they did what he said. The Guild gave in. (Dune)

Feyd-Rautha demanded a duel to the death. Paul fought him, saw through the poisoned needle Feyd had hidden on him, and killed him. Count Hasimir Fenring, ordered to fight next, refused. The duel is covered in full on Paul vs Feyd-Rautha. (Dune)

Then Paul gave his terms. Shaddam would abdicate and go into exile on Salusa Secundus. Paul would marry Irulan and rule through her claim. Chani was hurt, but Paul promised her that Irulan would have nothing from him but the title. Jessica, who had spent her life as the Duke's concubine, told Chani that history would call the two of them wives, and those are the last words of the book. (Dune)

What sort of Emperor he became#

Dune Messiah opens twelve years later. Paul rules from Arrakis as Emperor and as a god to his followers, with a priesthood, the Qizarate, running the religion built around him. The jihad he foresaw is still being fought across the universe. Irulan is his wife in name only, and Chani is his real partner. (Dune Messiah)

His throne still rests on the same thing it did on the day he won it: the spice, and the Fremen legions who would follow him anywhere. The twelve years between Dune and Dune Messiah fills in what the novels say about that gap. (Dune Messiah)

How Dune: Part Two tells it#

Villeneuve's film keeps the outline and changes the details. Paul sends Shaddam a challenge to come to Arrakis. The Fremen breach the rock walls around the imperial camp with atomics during a storm and ride worms through. Paul kills the Baron himself, then kills Feyd-Rautha in a duel. (Dune: Part Two)

He tells Shaddam he will rule through marriage to Irulan, threatens to destroy the spice fields with atomics if anyone stands against him, and the Emperor kneels and kisses his ring. But the Great Houses in orbit refuse to accept him, and Paul sends the Fremen to war against them. In the film, becoming Emperor and starting the holy war happen in the same scene. (Dune: Part Two)

For the whole final chapter of the novel, see the Dune ending explained. (Dune)