This page of the guide to The Elder Scrolls V: Skyrim features the walkthrough for the initial part of the main quest The World-Eater's Eyrie. As part of this quest, the hero must set free the dragon Odahviing¬†and then convince it to take the protagonist to Skuldafn Temple.
New main objective: Set Odahviing free
Remain at where you caught Odahviing, i.e. Dragonsreach, Great Porch. Use the stairs to reach the south-east balcony and talk with the Whiterun Guard there (screen above). Confirm that you want to free the dragon, despite his warnings. Wait for the dragon to be set free.
New main objective: Talk to Odahviing
Go down and head to the observation point, where Odahviing should be. Talk with the dragon, who according to your deal, will want to take you to the Skuldafn Temple. Note! Before confirming the will of heading to the temple (upper dialogue option - screen above), it's worth to make certain preparations. Above all you need to know that you will go there on your own. You should stock up on items increasing your fire, cold and lightning resistance and also lots of potions and other supplies. You will be leaving Skyrim for quite long and therefore you won't be able to visit any merchant or hideout. After confirming that you're ready, you will be transported to the Skuldafn Temple.