The Dwarf Origin story is not a bright one. As a casteless Dwarf you'll have a hard road ahead of you. This guide will help guide you through the origin story of the Dwarf Commoner.
From Rags to...
If anything, the title of your lot in life - that of a supposed Dwarf Commoner - is deceiving. As you discover quickly in the Dwarf Commoner origin story, you lot in life is the lowest of the low. You are a Dwarf without a caste, which in Dwarven culture makes you scum.
The beginning of the Dwarf Commoner origin story involves a long conversation between yourself, your sister Rica, and a thug named Beraht. This initial conversation largely exists to give backstory, so despite his ruthless nature Beraht takes it easy on you if you give him lip. After your conversation with Beraht, you should talk to your sister, Rica, and to your mother, Kalah, both of whom can give you more backstory.
Dust Town
When you exit into Dust Town you will meet a Dwarf named Leske, a buddy of the player character. In addition to some friendly conversation, Leske will give you all the details about your mission from Beraht. You are to find a smuggler who Beraht thinks is taking a cut and deal with him.
There are a few Dwarves you can speak to before heading off to complete your new quest, so feel free to explore the areas you can gain access to. There is not anything special, but the conversations help flesh out the story, so I suggest taking the time to poke around.
The Smuggler
Once you're ready, head to the tavern to find the smuggler, whose name is Oskias. Speak to the tavern owner and he'll point out Oskias for you once he realizes you're Beraht's thugs and not the typical low-life.
The smuggler will also become very skittish once he realize that you're there to talk to him about his activities. You can either kill him, which earlier conversations indicate is preferable to Beraht, or you can let him go. You'll get the goods you need to bring back to Beraht either way, and no one will try to stop you.
The Proving
Once you're dealt with the smuggler you'll need to go tell Beraht of what happened. He will give you a hard time if you didn't kill Oskias but won't harm you. In either case he'll tell you that he has a new mission for you and Leske. Beraht has bet a lot of money that a certain fighter will win a fight at an event called The Proving and he wants to make sure the right fighter wins.
Head to The Proving and get by the guard by providing him with the pass Beraht gave you. There are a few people to speak to along the way, and you can meet Gray Warden Duncan for the first time. Whenever you're ready, head down to the fighter's barracks. You'll find that the fighter Beraht has put his bets on is passed out drunk.
You have only one option - dawn the fighter's gear and enter The Proving in his place. He has full plate armor, so no one will be able to notice. Your only other task before heading into the Proving is to speak to another fighter named Mainar. This will allow Leske to drug Mainar's drink, giving you an advantage.