Friendship with Fenris can generally be earned by siding against any mages, not coddling him when he speaks of his problems but understanding them, being ruthless to slavers and being kind to the innocents- particularly elves and slaves- in the game.
Bait and Switch: At the end of the quest, a non-mage Hawke says, "I'm well aware." (only available to a non-mage Hawke who brought a mage along during the second half of this quest.) (+10)
Bait and Switch: At the end of the quest, Hawke investigates and says, "Why is Danarius after you?" and then chooses the diplomatic options. (+5)
Note: If Hawke is a mage, there is no way to avoid rivalry gain at the end of this quest. However, this option will knock five rivalry points off the final score. For example if "Survival." was chosen in response to Fenris's first question, the final rivalry score will only be (+5).
Enemies Among Us: When talking to Cullen upon returning to the Gallows (after completing the quest), choose: "I support the Templars." (+5)
Investigate > "How long since you escaped?" > "You've been alone?" > "Are you sure?" > "Good plan."
"You could make a home here." (+20)
Fenris Recruited: Alternatively, if Hawke follows the steps shown above but ignores the Investigate conversation options, instead skipping right to "You could make a home here." (+10)
The Gallows: If Fenris is in the party when Hawke returns to the Gallows for the first time and says, "The Circle is necessary." (+5)
Long Way Home: When Merrill opens the barrier with blood magic, Hawke says, "The demon, you mean." (+10)
Long Way Home: At the end of the quest, Merrill asks Hawke if he/she will visit soon and Hawke says, "I don't think so." (+5)
Alone: In the first dialogue choice, pick either the Diplomatic or Witty option and then agree at the first opportunity to go with him to meet Varania at the Hanged Man (+5)
Bait and Switch: Upon completion of the quest, if Hawke is a mage, Fenris will question your motives when you recruit him. "Seeking power" will earn (+25); "Survival" and "Find Out" yield (+10); nothing earns (+15); asking if it will be a problem earns (+20). Non-Mage Hawke, choosing "That's not your concern" or defending the mage in party earns (+5)
Tranquility: When speaking with Anders for the first time, choosing to investigate and selecting the "Help him escape the Circle?" option, answer "The mages need their freedom" (+10). If playing as a mage, choosing "I help all my fellow mages" (+10).
Wayward Son: Stating that you wish to help Feynriel when accepting the quest from Ser Thrask in the Gallows (+10)
Wayward Son: Let Fenris get information out of Danzig and then spare him (+10)
Wayward Son: Defer to Varric when dealing with the slaver holding Feynriel hostage and then doesn't kill him afterwards (+10)
Wayward Son: Tell the slaver holding Feynriel hostage that you can work something out (+10)
Wayward Son: Allow Feynriel to go to the Dalish (+10)
Gallows: With Fenris in the party: Earn points depending on your answer. For the most, pick: "It is wrong to oppress Mages." (+15). For the least, pick: "The Circle doesn't work." (+5)
During personal conversations at his mansion, Fenris rewards pitying phrases like "I'm sorry" with (+5), and harsh remarks like "Get over it" with (+10).
Alone: Choosing the 'Witty' dialogue option followed by asking him why he's following up on this, instead of immediately accepting or rejecting his request (+5)
Alone: Offer to negotiate an arrangement with Danarius (+10)