This quest becomes available after Hawke's first encounter with Varric in Hightown.
Travel to the Hanged Man in Lowtown and speak with Varric. He will inform Hawke that they need a suitable entrance into the Deep Roads, and that a Grey Warden who might know of one recently arrived in Kirkwall from Ferelden along with the other refugees. The quest is complete once the conversation between Hawke and Varric is finished.
Depending on the tone of Hawke's final dialogue choice, Varric's approval will change as follows:
Diplomatic (top choice):
Humorous (middle choice):
Aggressive (bottom choice):