Now that you have the Jarl’s aid, you’re going to need a way to get a dragon to come to you at Dragonsreach. This turns out to be fairly simple- if you had to have peace talks, then Esbern will approach you afterwards. If not, you can go to him or climb up the Throat of the World to find Paarthurnax again. Whichever of the two you speak with will explain to you that each dragon’s name is itself a set of three Words of Power- making each dragon a Shout in and of themselves. They will then teach you the name of one of the dragons that Alduin has already resurrected: Odahviing, or Snow Hunter Wing.
Knowing this, you now merely need to head to Dragonsreach in Whiterun to be ready. Speak to the Jarl in his court- he will let you know that he is prepared, and ask if you are as well. Should you answer yes, he and his aid will head to the balcony of Dragonsreach. You will need to head there as well. Both will express their readiness, and then the Jarl inquires if you have a way to bring a dragon there. The answer, of course, is ‘yes’, which you prove by Shouting Odahviing’s name over the edge of the battlements.
There is a short wait after you Shout, and then Odahviing arrives, announcing his presence by swooping in and more likely than not taking out one of the guards. He will then fly around over the cliff in back of Whiterun, occasionally hovering to blast you with his breath weapon. While you can injure him, you should not be trying to kill him- rather than pepper him with arrows and spells, hit him with the Dragonrend shout. This will force him to land on the balcony and fight you snout-to-sword.
Draw him in towards the back of the balcony, and when he’s in position under the gigantic stocks, the guards posted up above will trigger the trap, which drops down, pins him to the floor, and clamps shut around his throat! Don’t worry too much about accidentally killing him, he’s essentially unkillable thanks to a thick coating of plotdevicium, but don’t worry about wearing him down either. Save your potions and such and just force him to chase you around until he’s in the right position for the stocks.
Although he is humiliated by being trapped with such a ‘low’ trick, Odahviing is impressed by your cunning and might, and is actually fairly affable. The red dragon will answer your questions perhaps a bit too eagerly, so you’ll have to get him back on track when he goes off on a tangent about how the other dragons feel regarding Alduin. Once you press him enough, he will explain that Alduin has headed to Sovngarde to regain his strength by devouring the souls of the dead, tho door of which is in Skuldafn. He asks to be freed, to which you can respond either by demanding he serve you or explaining that you will free him when Alduin is dead.
Either way, he then points out that you cannot reach Skuldafn.... because you cannot fly. He offers to fly you there, but points out that you will have to free him in order for him to do so.