AN UNLIKELY SCHOLAR
Dagna (Orzammar Commons Map, L3)wants to join the Circle of Magi to study their history and lore, but knows that dwarves cannot use magic. She is a member of the smith caste, those dwarves responsible for creating the arms and armaments of Orzammar and working with lyrium.
Janar
At some unspecified point in her life, she found a scholarly fascination with the mages of Thedas and with the practice of magic despite being well aware that she could never become a mage herself.
When the Warden encounters her, she has been attempting to gain the attention of the Kinloch Hold for a number of years but with no success. She is well aware that leaving Orzammar would mean forsaking all claims to family and become casteless but appears to have no reservations about doing so if given the chance.
As a form of payment for studying amongst the mages, she offers all that she has learned of working with lyrium from the smith caste.
Walkthrough
When Dagna first makes her request, the Warden can agree to help her or refuse.
Agreeing to take her request to the circle will net (+2) from Wynne and (+1) from Leliana. Morrigan will also have a few comments but her approval does not change.
Dagna's father, Janar.
Runs a shop in the Orzammar Commons. If spoken to before Dagna has left for the Circle, he will ask that the Warden does not get involved as he wants his daughter to stay in Orzammar. The Warden can agree with his views and return to Dagna telling her that she should stay with her father. Dagna will be displeased and the quest will end.
Alternatively, travel to the Circle Tower. If it has not already been done, it will be necessary to complete the Broken Circle quest before broaching the subject of Dagna studying there.
Depending upon the choices the Warden makes, Dagna will or will not be able to study at the Circle of Magi.
If The Warden Sided with the Templars - Knight-Commander Greagoir will respond she cannot study at the Tower. It is also possible to skip asking Greagoir for permission and simply tell Dagna that the Circle was destroyed. In which case Dagna will make her own way to the tower.
If however the Warden Sided with the Mages - First Enchanter Irving will be open to the idea that she can study at the Tower.
Return to Dagna with the news.
Result
If Dagna has been accepted into the Circle Tower, she can be found there next time The Warden visits.
If you talk to Dagna's father after this quest and tell him she left for the Circle, he will be upset that she has become a surface dwarf and casteless. He will refuse to trade with The Warden and forces The Warden to leave his store.
Note: If you speak to Dagna's father after completing the quest without mentioning anything to him beforehand, he will still maintain his dialogue as if you had never done the quest at all. Simply avoid asking him about Dagna, and access to his shop will remain.
After agreeing to tell the Circle of Dagna's request: Leliana (+1), Wynne (+2)
Rewards
Assuming that you saved the mages in the Circle Tower and respond positively to Dagna's request, she will reward you with either a Lyrium potion (type depends on your level) or a Dweomer Rune (tier depends on your level) if you ask her for one. Requesting the "token of gratitude" also awards 100 XP.