Serana approaches you after Harkon is done with his speech. She asks you if you have any idea on how you are going to find a Moth Priest. Skyrim's a pretty big place.

You can ask her:
Where would a Moth Priest actually go?
Do you have any ideas?

Ask her where a Moth Priest would go. She tells you that the College of Winterhold would be the first place she would think to go for any kind of magic or historical thing. The wizards know about all kinds of things that people probably shouldn't know about. Serana says she will accompany you.

This adds the optional objective:
Visit the College of Winterhold to ask about the Moth Priest

Your quest log has also been updated:

Prophet
Eager to unlock the secrets of an ancient prophecy thought to be hidden withing Serana's Elder Scroll, Harkon has ordered his court to find a Moth Priest

Note: You just have to do ONE of the optional objectives below. Once you find out from any of the NPCs about the location of the Moth Priest, the other optional objectives will be marked as completed as well.

Asking a Carriage Driver
Ask any carriage driver outside a stable if he has seen a Moth Priest. He tells you he is not sure if he had seen one. Try persuading him or bribing him. You learn that a Moth Priest had asked the driver to take him to the Dragon Bridge.

Asking an Innkeeper
You can ask an innkeeper in any major city if he has seen a Moth Priest. You find out that there was a Moth Priest who had stayed in the inn, on his way to the Dragon Bridge

Visiting the College of Winterhold
Fast Travel to the College of Winterhold. Talk to Urag gro-Shub.Tell him you need to find a Moth Priest. He says that the obvious answer is to go to the Imperial City. The Moth Priests make their home in the White Gold Tower. Sometimes they go out looking for Elder Scrolls. Lucky for you, there's a Moth Priest in Skyrim right now, doing just that. He stopped in to do some research in the library, then left for Dragon Bridge. If you hurry, you might catch him there.

The next objective in the quest unlocks:
Ask people in Dragon Bridge if they saw the Moth Priest.