In this quest your objective is to trap Odahviing in Dragon’s reach and interrogate him. Firstly you have to acquire Jarl Balgruuf the Greater’s premission to trap a dragon in Dragonsreach. If you haven’t settled the peace in skyrim you have to negotiate a truce in High Hrothgar. Be sure to keep a neutral stand point to reach a fast agreement.
Afterwards you have to travel back to Sky Haven Temple to learn the required shout, “Snow Call Dragon”, from Esbern.
Then you will have to go back to Dragonsreach in Whiterun and use that shout. Odahviing will come. Instead of fiting him, keep walking backwards into Dragonsreach and lure him in. Eventually the trap will fall.
Next you will have to negotiate with him that he shows you how to find Alduin. Don’t worry, he isn’t going to turn on his word, once you release him he flies you to the required place.
That is the end of this quest.