Quest: A Daedra's Best Friend
Reward: The Rueful Axe or Masque of Clavicus Vile
Level requirement: 10
Speak to Lod (misc): A guard will stop you when you enter Falkreath and ask if you have seen a dog. He will tell you to speak to Lod the Blacksmith about it.
Find the dog outside Falkreath (misc): Speak to the dog (Barbas) and he will ask for your help reuniting him with his master Clavicus Vile by travelling there with him.
Travel with barbas to the Shrine of Clavicus Vile: Trek to the shrine with Barbas, or go later, it doesn't matter. Fight through Haemar's Shame against vampires and their thralls, and even a frostbite spider before reaching the shrine.
Retrieve the Rueful Axe with Barbas: Clavicus Vile will ask you to retrieve the Rueful Axe from Rimerock Burrow in Haafinger. With or without Barbas, travel to the small cavern West of Solitude and kill Sebastian Lort and his pet atronarch before claiming the axe.
Return to the shrine of Clavicus Vile with Barbas and the Rueful Axe: Return and Clavicus will offer to let you keep the axe if you kill Barbas with it.
Give the Rueful Axe to Clavicus Vile OR Kill Barbas with the Rueful Axe: IMPORTANT: If you choose to kill Barbas and keep the Axe, it does NOT count toward the 15 daedric artifacts needed for the "Oblivion Walker" achievement/trophy. Either kill Barbas or refuse, at which point Clavicus will give you the Masque of Clavicus Vile, a badass looking helmet.