The Rise of Skywalker doesn't explicitly say how Palpatine escaped death, although it does drop a couple of hints. When Kylo visits Exegol for the first time, he finds Supreme Leader Snoke clones floating in tubes. Later, Dominic Monaghan's character, Beaumont Kin, offers a handful of theories of his own: "Dark science. Cloning. Secrets only the Sith knew."
As it turns out, Beaumont nailed it — Palpatine's return relies on all three. Like the Star Wars movie novelizations, Rae Carson's The Rise of Skywalker: Expanded Edition fleshes out the story that we saw on the big screen. That includes Palpatine's return. Basically? He used clones. While ruling the galaxy, Palpatine set up a secret cloning lab on the planet Exegol. As he fell down the second Death Star's reactor shaft in Return of the Jedi, Palpatine used the Force to project his consciousness into a new body on the far-off Sith stronghold, a skill that Carson implies he learned from his former master, Darth Plagueis.
Unfortunately, things didn't go exactly as Palpatine had planned. "The secret place had not completed its preparations," Carson writes. "The transfer was imperfect, and the cloned body wasn't enough." Apparently, the dark side takes a big physical toll, and Palpatine's new vessel burned out quickly. And so, as the New Republic took control of the galaxy and the First Order accumulated power in the Unknown Regions, Palpatine's Sith followers worked tirelessly to create the Emperor a new, healthier, and more permanent body.
Most of those experiments failed. One didn't. At least, not exactly. "One genetic strandcast lived," Carson writes. "Thrived, even. A not-quite-identical clone. His 'son.'" Still, even that body wasn't perfect. While the clone survived the Sith experiments, he couldn't use the Force. That weakness disgusted Palpatine. Instead of using the clone as a host, the former Emperor found another use for him. He set his "son" free, so it could "continu[e] the bloodline through more natural methods."
That worked. Palpatine's son met a lady and had a daughter — that's Rey — whose powers met Palpatine's standards. And so, the Sith lord began making plans to capture Rey and take over her body. As we've seen, that didn't exactly pan out.
