To keep it simple, I'm mostly gonna use the same names from the Force Awakens
The New Republic: They've established a successful political system after the fall of the Empire. They've enjoyed relative peace for 30 years but their drive to expand has led to some discord for some systems who believe the Republic is becoming too corrupt with their power. This leads to the creation of the First Order.
First Order: More of a terrorist group then a full fledged military dictatorship, similar to ISIS. They're responsible for different attacks throughout the galaxy. The Republic views them more as a nuisance than a legit threat. Their figure head is a charismatic leader, similar to Osama.
Luke: He's created a new Jedi Academy but as he's gotten older he's less interested in politics and the inner workings of the Republic, more focused on training new Jedi
Leia: She's still a leader in the Republic but it's more of a counselor type role overseeing the senate
Han: He's a military leader for the Republic
Poe: I'd make him Han and Leia's son, a rising pilot and mission leader in the Republic trying to get out of his father's shadow
Rey - Backstory: Luke's daughter who was training to become a Jedi but ended up quitting and becoming a doctor on a planet for refugees. We find out later the reason why she left. Her mother and older brother (who is also a Jedi) fell ill with a mysterious disease. She was convinced the disease could be treated by practical medicine but Luke believed the illness was caused by a Dark force and tried to heal them through the force. He failed to save them however and they both died, leading to Rey becoming disillusioned with the force and leaving the Jedi Order.
Kylo Ren - Backstory: He was born Ben Skywalker, Luke's son who was training to become a Jedi but fell ill and died. After his death, the spirit of Darth Plageuis resurrects him and offers him a deal. Commit to the dark side of the force and do his bidding and he'll give him the power to resurrect his mother. Ben agrees, trains in the dark side and becomes Kylo Ren. He works in the shadows and isn't out in the open but he's the driving force behind the First Order. Luke isn't aware of him at the start of the movie
Finn - Backstory: He's the son of two rebels who led a faction against the First Order when they tried to occupy his home planet. Kylo Ren leads a team of elite First Order fighters who annihilate the faction and kill Finn's parents. Kylo spares Finn's life when Finn tries to fight back. He's impressed with Finn's rage and believes he has the potential to become his apprentice. Kylo takes Finn prisoner and tells him that if he wants to take his revenge and kill him, he has to fully commit to the dark side of the Force. Kylo takes advantage of Finn's desire for revenge and trains him. This all happens before the film begins but is revealed later through flashback.
Darth Plageuis: He’s not fully formed and weakened and more of a spirit who guides and directs Kylo Ren
Story
Starts out with Poe leading a raid from the Republic to destroy a First Order base. The raid fails however and we find out that the First Order received information tipping them off that the raid was coming leading to speculation that there's a traitor among the Republic. All of Poe's squadron is killed and Poe is captured
Finn is a prisoner on the base, we see him training in the dark side of the force as Kylo Ren watches from a hologram. During the raid however, power is briefly knocked out at the base and Finn manages to escape. He rescues Poe and realizing that Poe is with the Republic, he demands that Poe take him to see Luke Skywalker.
The two escape and head to the rendezvous point at a nearby planet but crash land during a storm. We find out that Rey has been on that planet for several years after quitting the Jedi order and has helped provide medical aid to sick refugees who fled their home planets because of the First Order.
Poe is injured in the crash and Finn seeks medical attention. That's when he runs into Rey who immediately recognizes Poe as her cousin. Meanwhile Kylo becomes convinced that Finn will never truly embrace the dark side and correctly deduces that he's searching for Luke after escaping. He doesn't want Luke to know about his existence yet so he sends First Order soldiers after Finn. This leads to a chase scene where Poe, Rey and Finn flee. They reach the rendezvous point and are saved by Han and Chewie who were waiting there in the Millennium Falcon the whole time
Han, Chewie, Poe, Finn and Rey arrive at the new home planet of the Republic. Could be Coruscant or something entirely new. We're introduced to the inner workings of the Republic and see that there's tension between the new leader of the new Republic and the old leader who he defeated in the election. New leader is more about keeping the peace and compassion, old leader was more aggressive and militaristic. Leia is trying to keep the peace so that the Republic doesn't break apart. New leader also has a military advisor who influences most of his decisions.
Big controversy is the new leader's unwillingness to kill surviving members of the Empire who were put on trial for war crimes. Instead they're sentenced to a prison planet that few members of the Republic have seen. Poe also reports about the failed attack leading to more speculation that there's a traitor within the Republic
Finn meets Luke and tells him his story, reveals the existence of Kylo Ren. Finn wants Luke to help him find Kylo so that he can take his revenge. Luke wants to complete his training and undo the years of training in the dark side of the force. Rey also reunites with Luke and we see the tension between them and the anger she still feels for him. She ends up revealing her backstory to Finn and the two begin to bond. They both plan on leaving the home planet but all travel is blocked due to a major announcement coming.
Wanting to end the in-fighting and tension within the Republic the new leader announces they've discovered the location of the First Order base through information provided by his military advisor and gains support from the Senate to launch a full-scale invasion.
Han and Poe lead the invasion on what they believe to be the home planet of the First Order. The planet ends up being abandoned however and it's rigged with explosives. Explosives go off and destroy the entire Republic fleet except for Han, Chewie and Poe
It turns out the military advisor was secretly working for the Empire the entire time and the First Order was a means to distract the Republic as the Empire rebuilt in the background. The prison planet was actually the new home planet where the Empire has rebuilt its entire army over a 30 year period. With the New Republic fleet gone, the newly rebuilt Empire launches a full-scale attack and invades the New Republic's home world. Finn and Rey manage to rescue members of the senate while Luke and his Jedi trainees rescue as many citizens as they can during the invasion. They all retreat to the Haven which is basically a safe house with defense shields protecting them. It’s during this time when Rey and Luke reconcile. The surviving members of the New Republic reconcile as well.
The Empire forms a blockade around the Republic’s home planet and blocks all communication. Leia manages to connect with Han through the Force however. Han, Poe and Chewie travel to a planet full of former members of the Rebellion. I’m thinking it’s similar to the Army Reserve where they’re called upon in cases of emergency. Han convinces them to send in a squadron to fight the newly formed Empire.
Realizing that they can’t penetrate the Haven, the Empire asks Kylo and the First Order for help. Kylo consults with Darth Plageuis who tells him that he’s ready to confront Luke Skywalker. Kylo and his troops deactivate the defense shields and infiltrate the Haven. It’s here where we really see Kylo’s true power as he takes out the Jedi trainees one by one
Han and the squadron arrive but are unable to break through the blockade. Han and Chewie then share a final moment with Poe as well as Leia via the force. Han then activates his hyper drive and flies head on into the main blockade ship with the Millennium Falcon, destroying the ship, breaking the blockade and sacrificing his life in the process. The Rebel forces breakthrough and begin attacking the Imperial forces on the ground leading to a huge battle
Finn confronts Kylo who has broken through the Haven. The two fight and Kylo notices that Finn is holding back his rage and anger, Kylo tries tempting him to the dark side telling him that his only chance of victory is embracing his rage. Finn briefly gives in and starts to win the fight. But he then remembers what Luke told him and starts to calm himself. Kylo then taps into the dark side and unleashes on Finn. He defeats Finn similarly to how he did in the Force Awakens, slashing him across the back. Kylo then confronts Luke and reveals himself to be Luke’s son. Luke is shocked and the two begin to duel but reach a stand still. Luke then stops fighting and decides to sacrifice himself similar to how Obi Wan did vs. Vader. Kylo has the chance to kill him but can’t bring himself to kill his father. So he retreats
Elsewhere as more First Order troops overrun the Haven and approach the surviving members of the Senate, Rey finally picks up a light saber and battles them. And we see how powerful she is as a Jedi.
The Rebels turn the tide and defeat the Imperial forces who retreat and regroup. As Kylo leaves, Rey sees him and in a state of shock realizes her brother is somehow still alive.
We end with Darth Plageius admonishing Kylo Ren for his failure. We then see the perfectly preserved body of Kylo’s mother. He promises her that he’ll bring her back.
After being defeated by Kylo, Finn realizes he still needs more training and agrees to stay with Luke. Rey has also decided to complete her training. The two stay with Luke as Poe and the surviving New Republic forces go off to battle the newly-formed Empire.