The Beginning
You start out as a prisoner, as you do in every TES game. You're supposedly going to be executed for trying to cross the border; not so much because you did anything wrong, but because you happened to be right near a group of dangerous rebels and the commanding officer of the Legion just doesn't give a [censored] if you were involved or not. Luckily, as you face your execution, a dragon arrives and stirs up so much trouble that you're able to escape with either the help of a rebel or a Legion officer. Both of them will lead you to the town of Riverwood, which agrees to help you and give you a place to sleep, but also asks you to alert the Jarl of Whiterun of the danger, so he can send more guards to defend Riverwood.
You go to the Jarl and he agrees, while simultaneously asking you to help his Court wizard study the dragons. The Court Wizard requests that you go fetch some stone tablet that'll help with his research. As you go there, you discover your first world wall and absorb the words like a freaking dictionary sponge. When you return, a dragon is conveniently attacking a tower near Whiterun. Once it's killed, you absorb his soul like a sponge and everyone calls you Dragonborn. On your way to report to the Jarl, the greybeards, who are LOUD AS HELL, shout from the top of the Throat of the World and say "hey we want you to visit us lol." Once you go there, they tell you that they're sworn to train all Dragonborn in the way of the voice, give you brief training, then send you on a fetch quest. Why? Because apparently all Dragonborn do fetch quests. When you go to do the fetch quest however, the item you seek isn't there, and in it's place, you find a note from "a friend" wanting to meet you.
The Middle
When you go to meet this friend, you find out she's a member of the Blades; a dying organization who was sworn to defend and serve Dragonborns of olden days. When you first meet her, she wants you to kill a dragon to prove you're dragonborn. Why? Because apparently Nords have the memories of friggin' goldfish so everybody forgets major events and thus the news of your battle in Whiterun never reached anyone; infact, everyone simply forgot about it. So, you go to kill a dragon, then she says "wow u did it." Afterwards she theorizes the Thalmor are somehow behind the dragons, since the Thalmor hate humans and....well apparently the dragons are only a threat to humans or something. Iunno. So she comes up with this elaborate plan for you to break into the Thalmor embassy and steal their documents, then once you do and bring them back to her she says "LOL NVM they're as clueless about the dragons as we are, oh well." Then it occurs to her that maybe instead of making baseless accusations, she should have you look for her old comrade. Why? Because he's a super-genius who has a degree in dragonology. Oh and also his life is in danger so you should probably hurry. You find him, rescue him, and sure enough he knows where you might be able to find some clues to explain the return of the dragons. Sure enough, he leads you to a wall of prophecy that depicts the history of the world and some of it's future (conveniently cutting off after Skyrim's point in time, cause yknow, they haven't planned the next games yet), and the future depicts dragonborn being the only thing that can stop the dragons and the end of the world.
Then the old coot tells you there's this special shout that is the key to destroying the dragons. Suddenly it occurs to you that you know some dudes who could probably teach you every shout you could possibly need, so you should stop dikeing around with secret agents and just ask them how to defeat the dragon. Then you return to the Greybeards. The Greybeards tell you they know of the shout you speak of, but don't know it themselves because they believe it to be dangerous. They tell you to climb to the top of the mountain to meet their master, who turns out to be a dragon himself. You ask him if he could teach you the shout, to which he replies "motha [censored]a I'm a god dang dragon and you think I'd learn a shout to kill myself?" He does recommend though that you obtain an Elder Scroll, which would allow you to look through time itself and see the past, where three heroes used the shout you need to defeat Alduin. With that, you could learn it yourself. He tells you to talk to the mages guild cuz mages r smart, and they point you in the direction of an Elder Scroll.
The Ending
Once you obtain it and bring it to the Throat of the World, it allows you to look back in time and witness the battle against Alduin in times of old. You learn the shout, but also learn that their shout didn't actually DESTROY alduin, but simply sent him back in time (to your time, obviously), delaying the end of the world but not stopping it. Alduin apparently somehow knows everything you do, so he shows up and says "wtf how dare you learn that crap!!" and you guys battle. The dragon leader of the Greybeards says "damn man, you didn't defeat him, he just went to regain strength but I dunno where to find him." He then suggest that the only way to find him is to get another loyal dragon of Alduin to betray him and tell you. He suggests provoking a certain dragon by dissing his mother, because this particular dragon hates it when haters be dissin' on his momma and will certainly react. For this though, you'll have to trap him in the dragon temple thingy in Whiterun, and before the Jarl will let you do that, he wants the Civil war guys to agree to a temporary truce. You talk to them, they truce. Yay. Then you trap that dragon. Yay. He's so humiliated by being trapped that he agrees to help you. Yay.
Apparently Alduin has gone to Sovngarde (the afterlife) to feed on souls and regain his strength, and apparently there's a portal to Sovngarde nearby. He takes you there, you fight a bit, then go through.
***This is about the point where the storyline goes completely down the [censored]ter.
You enter Sovngarde and see Alduin feasting on souls. You decide that you'll need to talk to the heroes of Sovngarde about defeating Alduin once and for all. They're in this beer hall called the Hall of Valor, meant for only the most worthy of warriors. You have to prove yourself to it's gatekeeper, then he lets you in.
When you get in, you meet Ysgramor. Ysgramor is a pretty famous character. You hear his name all throughout the game. You hear about how he did this and that in history and was super important for Nordic culture. You also hear that Shor, Ysmir and a couple other major figures should be in the Hall of Valor. So there you are, Ysgramor right in front of you, and what does he talk to you about? "Hey, you should talk to those other guys. Not me." No dialog options, no questions you can ask him, no nothing.
Imagine if you will for a moment, if Lonesome Road were to come out, and instead of Ulysses having all this dialog, holotapes and other stuff revealing who he is, he says literally nothing until you meet him, and then when you meet him he says "you destroyed my home so now I'm going to blow up the world," and then you fight. That's about how disappointing it is to meet Ysgramor, and to find out you WON'T even be meeting Shor or Ysmir, even though they're there.
So after he points you to the other guys (the three warriors who originally defeated Alduin), they say "sure we'll help."
You go outside and get ready to fight, except one of them states "we can't fight him in all this fog, let's clear it out!" The area is covered in fog and you know a shout to clear fog, so all four of you use it. The fog clears, then five seconds later you hear Alduin shout something and the fog returns.
"His voice is strong! We'll need more power!" says one of your comrades. So you yell at the fog again. BTW, the shout to clear fog sounds like "Bakawk," so you all sound like chickens, so that's great too. After a 10 second pause, Alduin does his shout and the fog returns.
"He's weakening, Shout again!" says your comrade. So you shout at the fog again. You're shouting at a [censored] cloud. Then you hear Alduin again, and sure enough, the fog returns.
"There, he's losing power! One more should do it!" your comrade says. You shout at the fog again. This time it doesn't come back. You've defeated the fog.
At this point Alduin shows up to fight. Except, you've already fought him once before, and that was practically one versus one. The first fight was semi-difficult and you had to learn his weakness. Now you have four comrades. He basically lands and starts fighting one of them, then you're free to swing your sword at him and quickly kill him. Really easy. He dies. Then the gatekeeper to the beer hall says "thank you, but you do not belong here. This place is for dead people, so gtfo." If you try to talk to any NPCs to hear reactions from them, they have none. Also the beer hall locked the door on you cause they hate you, so you can't go back in. So there's no point in staying; just leave.
Once you leave, you find yourself on top of the Throat of the World. There's a bunch of dragons there. The dragons basically say "hey you killed Alduin, he was kind of a [censored] so we're really happy. We're gonna fly around in circles to celebrate, yaaaaay." Then they fly around in circles.
....THAT'S THE END.
Nothing else happens. You don't get a reward, dragons still attack you and only two NPCs will react to what you've done. Both of them will basically say "you defeated him? Good job" and then they go on with their lives....And that's it. There's literally nothing more. You spend 5 minutes shouting at a cloud, a handful of people say "good job," then you get on with your life. Again, no reward, no reaction from anybody, no nothing. You do TECHNICALLY get a reward, but it's a shout that's SOOOOOO expensive to use (like if you use it, you can't use another shout (ANY other shout) for the rest of the day, compared to several other useful ones that have like a 30 second cooldown) that you'd never use it.
Like, I don't even know what to say about the ending. It was just horrible.