Dragon Bridge is located between Solitude and Markarth. If you have already been to Dragon Bridge (some Dark Brotherhood quests take you there) then just fast travel. Otherwise, go to Solitude and from there head Southwest to Dragon Bridge.

Ask any of the people there, if they know anything about a Moth Priest visiting Dragon Bridge. They tell you to try asking one of the guards. Find a guard (Imperial Soldier or Stormcloak Soldier) and inquire about the Moth Priest. The guard tells you about one that rode through town not long ago with an escort of soldiers. They didn't stop, just headed south across the Dragon Bridge.

Your objective now is to search along the road that leads south from Dragon Bridge. Soon you reach an overturned carriage. Investigate the scene of the attack. There is a note on the body of one of the dead vampires near the carriage. Read the Vampire's Note.

Vampire's Note
I have new orders for you. Prepare an ambush just south of the Dragon Bridge. Take the Moth Priest to Forebears' Holdout for safekeeping until I can break his will.

Your next task is to capture the Moth Priest. Go to the southeast and locate Forebears' Holdout. There are lots of Dawnguards in this cavern, kill any you encounter. There are also Armored Trolls here. Approach a blue barrier that is holding the Moth Priest prisoner. Your objective now is to deactivate the Magic Barrier. Search the body of Malkus near it. Loot the Weystone Focus, then put it on the Weystone Source above. This will cause the magic barrier to become deactivated. Defeat the Enthralled Moth Priest, Dexion Evicus. When he is weak, use your vampire's seduction power on the Moth Priest.

From your powers menu select the following power:

Vampire's Seduction
Creatures and people up to level 10 won't fight for 30 seconds

(Note: If you do not have that power, you need to go out and wait a few days in the sunlight until you gain it. Also if you miss, you find out that you can only use this power once a day. In this case, just wait 24 hours and try again.)

After using the seduction power, feed on the Moth Priest to make him your thrall. Then, command the Moth Priest to go to Volkihar Castle. Talk to him and give him the order. Tell him the castle is off the norhern coast of Skyrim, due west of Solitude.

Report your success to Harkon. Tell him you have made the Moth Priest your Thrall.