This mission is a long way walk. Find some bonfire so that on the next time you go back near that spot, you can do fast travel. Once you reach your destination, video clip will show and you have to tame the owl.
First attempt, walk until you see and reach the owl. He will disappear and you will ended flying. Note: left and right button are same but up and down are counter. Means that your up key is walking forward but if you are flying, up key is down.
For the last location, keep following him until he reach at the end and that’s the time you can tame. To call him, press “Z” (PC users). To spy up air if theres an enemy near by.