Questions and Answers

Acquisition
You get it automatically after completing the quest Tranquility.

Walkthrough
Head to the Hanged Man pub in Lowtown, and talk to Varric inside. Basically, all he wants to know is more in depth details on your story, you can also ask about his brother, about the expedition, and about him and his history.

Result
If you ask him questions, and answer him right your friendship will him go up, if you answer him rudely, his rivalry will.