New main objective: Learn Shout to call Odahviing
If during Season Unending you have taken part in the negotiations between the Legion and Stormcloaks, you won't even have to leave the conference room in the High Hrothgar. Just wait for Esbern to speak after the main part of the negotiation, giving you the Word of Power - Snow, Call Dragon, Word of Power - Hunter, Call Dragon and Word of Power - Wing, Call Dragon. Using it you will be able to call in a dragon, Odahviing to be precise.
If you didn't participate in the negotiations, as the Jarl has agreed to use his castle to catch the dragon, you will have more freedom. In such situation you can head to The Throat of the World and talk with Paarthurnax (assuming he's still alive; screen above) or to the Sky Haven Temple and speak with Esbern. Just like above, you will learn the Word of Power - Snow, Call Dragon, Word of Power - Hunter, Call Dragon and Word of Power - Wing, Call Dragon.
Regardless of the plot development, you will unlock the Call Dragon Shout.
New main objective: Prepare a trap for Odahviing
New main objective: Call Odahviing to Dragonsreach
Open the world map and fast travel to Dragonsreach. Afterwards locate the Jarl of Whiterun and confirm that you're ready to trap the dragon. Head to the north-east part of the location and open the gate to Dragonsreach, Great Porch (screen above).
After reaching the porch, head towards observation point on front of you (screen above). Press TAB, enter Magic and choose the Call Dragon Shout as active. Look towards the sky and hold down Z. Now you will have to be patient, as Odahviing will take some time before coming here. In the meantime, I'd suggest opening the Shouts menu and setting the Dragonrend Shout as active.
New main objective: Defeat and trap Odahviing
After Odahviing appears, you will have to act quick as the dragon is capable of dealing great fire damage. Wait for him to start flying towards you or stop in mid-air and hold down Z to use the Dragonrend Shout. If you have done everything properly, the well-known blue glow will appear around the dragon (screen above).
Quickly get away from the observation point, as the dragon should land there soon. Don't attack Odahviing, as you're not aiming at killing him. Instead, wait for him to start going your way (screen above). Hide behind the building elements, thanks to which you won't have to heal all the time.
Keep heading towards the gate leading to the main part of Jarl's estate, encouraging the dragon to follow you. Eventually the dragon should reach the big wooden construction and automatically become trapped (screen above).
New main objective: Interrogate Odahviing
Approach the trapped Odahviing to initiate a conversation (screen above). The dragon will confirm your fears, as Alduin has ran to Sovngarde and is eating mortal souls to recover strength. He will also tell you that the only way of reaching Sovngarde is by walking through the gate in the Skuldafn Temple. As the location can be only reached by dragons, you will have to agree to free him, in return for getting a ride to the temple. You will however take care of that during the next main quest.
Main quest unlocked: The World-Eater's Eyrie