Thancred asks you to go to Vesper Bay, where Alphinaud has requested your assistance.
This quest is available if you have completed the quest A Final Temptation.
Starting the Quest
Talk to Thancred in Horizon in Western Thanalan to begin the quest.
Speak with Alphinaud
Go west to Vesper Bay and talk to Alphinaud, who is west of the Waking Sands building.
Search for the Domans
Go southeast and go through the exit from Western Thanalan to Ul'dah. Use an Aetheryte to go to the Chamber of Rule. Go southwest to where the orange arrow is pointing in the minimap. Approach the group of refugees and there will be a cutscene.
Speak with Alphinaud at the Quicksand
Go northeast and use the aetheryte to go to the Adventurers' Guild. Go west and up the stairs and go through the door to the Quicksand. Talk to Alphinaud and there will be a cutscene.
Speak with Yugiri
Talk to Yugiri to proceed.
Speak with Momodi
Go southwest to the counter and talk to Momodi.
Deliver Momodi's Letters
Go northeast and go out through the door of the Quicksand. Go east to reach the Sapphire Avenue Exchange. Go east and talk to Fridurih to hand over Momodi's lette, then go east and talk to Katherine to hand over Momodi's Letter.
Speak with Momodi Again
Go west to the Steps of Nald, then go west and up the stairs to enter the Quicksand. Talk to Momodi to proceed.
Speak with Yugiri Again
Talk to Yugiri and there will be a cutscene.
Speak with Raubahn
Go northeast and go out through the door of the Quicksand. Use the aetheryte to go to the Chamber of Rule. Go southwest to find Raubahn. Talk to him to complete the quest. There will be a cutscene.
Next Main Scenario Quest
After you complete the quest, talk to Raubahn to accept the next quest: Promises to Keep.