Head into Dragonreach Castle and up to the Great Balcony. Stand on the edge of the Balcony and use your new Shout to summon Odahviing. He will come and attack you. Back up into the castle a little and he will land and follow you in. Move all the way back to the door and when he’s moved far enough in, he’ll be captured automatically. Talk to him now and you’ll bargain for a ride to fight Alduin. After the chat, talk to the guard above and to the right of to set him free. When you are ready, talk to Odahviing on the balcony and set off for Skuldafn Temple.