You can start this questline the second time you leave Brighthoof to the overworld map. You leave Brighthoof first to get a specific item and return afterwards. After you have finished the main quest "A Hard Day's Knight", the next main quest is "Thy Bard, with a Vengenace".
Instead of following the quest marker, turn right around a mountain and look for a quest marker next to a river. You need to finish a simple side quest to have a magic bridge appear. After you did that, cross that bridge and find two goblins on the left. Start their sidequest and enter Mount Craw. Follow the goblin's questline until the end. The final enemy can be a little tough. Your best bet is a corrosive weapon with a decent amount of spare ammo. There is a fast travel point right before the boss to if you want to level up or get some more ammo capacity from the blacksmith in Brighthoof.
I found the pistol "Goblin Repellant" very helpful. You can get it as a side mission reward for "A Farmer's Ardor"given to you by Flora in Queen's Gate" after you finished "Goblins in the garden". "Goblins in the garden" starts from a bounty board in Brighthoof.