Why Luke Has Been Gone So Long. Over the course of the movie we learn that Luke and his wife Mara Jade were training new Jedi when the Knights of Ren attacked and abducted Ben. They killed Mara, and in desperation Luke took her to Ahch-To, which was an ancient nexus of both the Light Side and the Dark. In denial of her death, he sought to call upon the Dark Side to resurrect her. He was moments from doing it when the Force ghost of his father appeared to him and pleaded for him to resist the power of the Dark Side, because even once restored, she would need to be kept alive by more rage and death. Luke ends up screaming and abandoning the ritual, releasing the Dark Side energy he'd called upon in a burst of telekinesis and lightning that obliterates his X-Wing and strands him there. Moreover, it strips him of his connection to the Force entirely. He has no powers.
Surprise Attack on Leia. The start of the movie has Leia arriving at a New Republic military base, planning to give a speech for morale. Finn is Leia's body man, the two of them clearly having bonded over the past few weeks over Han. Poe is getting a promotion and command of a squadron. Then the First Order suddenly attacks. (To be clear, there isn't a ragtag Resistance; this is just a small detachment of the overall New Republic military.) The whole place evacuates, Poe goes to fend off the attack, along with a bunch of ships, and the opening attack goes very similar, including the death of Paige Tico (Rose's sister).
The good guys load up, and after they blow up the Dreadnought, they try to flee by jumping to light speed. But Leia's ship ends up going in a completely different course. They realize their ship's navigation system has been sliced, and when they drop out of hyperspace, they're caught in an interdiction field created by First Order ships, so they can't jump again to light speed. They flee at sublight speeds, and Kylo leads a fighter attack, but hesitates at the last second, and Poe drives him off. Leia's ship manages to slip into a lightning-filled nebula to avoid detection, but they can't activate the ship's hyperdrive. They call for help, but it's unclear whether the signal got out. There might not be anyone who can rescue them.
Rey and Luke. Cut to Rey, finding Luke. Insert a line that she's been flying all across Ahch-To for weeks, trying to hail him, and it was only by chance that they spotted the wreck of his X-Wing. She assumes he crashed, but says he can come with her now. He refuses, and she stays around to try to persuade him and get the truth out of him. She starts having glimpses of Kylo Ren, and we intercut Rey's 'three lessons' on Ahch-To with Leia trying to find a way to survive.
Overcoming the Interdiction. They do have a shuttle that could manage to slip through the interdiction and fly for help. Leia's main ship will go in one direction to lure off the First Order fleet. She sends Finn, Poe, and Rose to Canto Bight, a planet that engineers the specs of First Order ships, so they might be able to find a way to bypass the interdiction. (The First Order star destroyers have powerful long range weapons, so their defense is to use interdiction to force any enemy vessels to drop out of hyperspace far enough away that they'll be obliterated before they can approach. Finn, Poe, and Rose will need to take out the interdiction field so New Republic allies can get in and save the day.)
Over the course of the movie we discover that Rose is actually a First Order sympathizer and spy for them, and she revealed that Leia would be here and gave the First Order a remote connection to the ship's hyperdrive. But she didn't realize her sister would die in the attack, and now she's having second thoughts. On Canto Bight she's clearly scornful of the excesses of the rich, which she blames on the Republic; but then she sees that the First Order abducts some of the children there, and she has a crisis of conscience about the complexity of the conflict.
Phasma tracks the trio to Canto Bight and captures Finn and Poe. Rose reveals she was a spy all along.
Kylo, Rey, and Luke. Snoke has linked Kylo to Rey to try to locate where Luke Skywalker is, because he wants to use him for nefarious purposes.
Kylo and Rey slowly grow closer during the movie, and the whole time we think Kylo is trying to recruit Rey to the Dark Side. She gets the message from Leia's ship that they're trapped, and the warning that anyone who tries to approach would be shot down before they could get close enough to attack. Rey tries to use this to motivate Luke to act, but he is convinced if they go, they'll all die, and he refuses. Rey gets enraged at him, accusing him of abandoning those he cares about the way her parents abandoned her, which is when Luke shares the full story about Mara's death. He's broken, and feels he doesn't have anything to live for.
Rey leaves anyway, and goes to distract Snoke, thinking perhaps that can help her friends escape.
Tied on a String. As Rey goes to Snoke (whose guards are Knights of Ren), Finn and Poe are brought back to Snoke's ship to be executed (mostly Finn, because he's a deserter). Finn gets a brief speech entreating the storm troopers not to be loyal to the First Order. During this, though, Rose slips away and sends a transmission to Leia's ship.
She managed to get schematics for Snoke's flagship, and using the same connection she set up earlier on Leia's hyperdrive, now Leia can control Snoke's hyperdrive. And his hyperdrive is slaved to the rest of the fleet.
Snoke gives his villainous monologue, which can include him taunting Rey for being a nothing child whose parents abandoned her. But he says he has plucked the location of Luke Skywalker from Rey's mind, and when they capture him, they shall offer him and Rey and a hundred other Force sensitive children as a sacrifice to restore to life his master: Darth Sidious.
Things play out similar to in the movie. The execution is about to happen, Leia plugs in coordinates, Snoke taunts Kylo to 'kill his enemy,' and just then Leia triggers the hyperdrive on all the First Order ships: aimed into the lightning-filled nebula. They fly for only a moment, before the impact with the nebula causes terrible damage. In the moment Snoke is distracted, Kylo betrays and kills him, and then Rey and Kylo fight off the guards.
The explosions also interrupt the execution, and Finn and Poe flee, aided by a rebellion in the ranks of the storm troopers. Phasma and Finn battle, and she's got the upper hand, but then the New Republic fleet arrives. While Phasma is momentarily distracted, Finn uses the Force somehow to escape, and so Phasma orders a retreat.
Up in the throne room, the battle is over, and Kylo asks her to join him. She thinks he wants to be just as evil as Snoke, but he explains that no, he has been working from within this whole time to earn the trust of Snoke, to find where Sidious is. He says that if Rey is with him, he might be able to wrest control of the Knights of Ren, and destroy the First Order from within. Rey says that she understands now why he killed Han, but she can see it's torn him apart. She begs him to come back to the light.
And he does. We redeem Kylo Ren in part 2 of the trilogy. Leia and her son reunite, and Rose's betrayal is forgiven. Finn introduces Poe to Rey, and is super stoked that he can use the Force.
Then Leia, Rey, and Ben returning to Luke on Ahch-To, and him being offered a chance of redemption too. He still doesn't have his Force powers, but he can help those who do to be free from the Dark Side.
We can get a montage around the galaxy of good stuff being tempered by bad news. Some storm troopers rebel and flee, but see a city being razed. Leia returns to Coruscant to cheers, but then oversees a commemoration of those lost so far. The First Order occupies Canto Bight but a slave kid demonstrates he can use the Force.
Our final scene, though, is Phasma and other Knights of Ren arriving on Exogol, and bowing to the crackling red Force ghost of Darth Sidious.