Once the Warden receives this quest, a new location appears on the World map, marked as Refugees. Travel to the location and fight the darkspawn, which consists of ten Hurlocks (including one Hurlock emissary) and three Genlocks. Once the fight is over (regardless of how many refugees survived) return to a Chantry representative for a reward.
Bug! Turning in multiple Chanter's Board quests at once will give you the reward for all of them, but only the last of them will show up on feedback. However, if you check your inventory, it will reflect that you get the full reward for each quest.
It is not required to save all or even any of the refugees in order to complete the quest. The reward is the same regardless of the number of survivors (with exception to gains from Stealing). The journal makes no special mention of saving all of the refugees, simply stating "You reported the fate of the refugees to the Chantry Board," and any rescued survivors offer the same generic dialogue ("Oh, thank you, Maker! Thank you, thank you!" for the men, "I thought we were done for, for certain," for the women). As long as there is at least one survivor, the journal update after all of the darkspawn are defeated will state that you have "rescued the refugees", and can report the "success" to the Chantry Board.
This quest's location can no longer be entered after updating the quest and leaving.
This quest's location is required for the Traveler achievement.