It's a rather simple quest of going back and forth from two areas. You will need to complete the Circle of Magi string first, unless you feel like doing the string as "part" of this quest. After speaking with the smith's daughter, you go to the Circle Tower and speak with the First Enchanter and tell him you know of a dwarf who wishes to study at the tower. He assents and you can go back to Orzammar and tell her of this news to which she leaves immediately. Her father is the shop keeper immediately to the left when entering the commons.
- CAUTION* If you tell her father, the shopkeeper, that his daughter has left for the Circle, he will get angry and refuse to do any business with you after that.
You can view detailed information on the quest from the Dragon Age: Origins Wikia.