How do I get custody of my fifteen year old daughter who lives with her mother but is not happy?

Sadly, without additional information is impossible answer your question. What you will have to do is confer with the domestic relations/family law attorney who will be able to review the factual situation and determine whether or not there is any likelihood under it that the custody of the child would be changed by the court. On the other hand, it is possible for the parents to reach an agreement to better serve the child generally that will be allowed and placed into an order of the court. Self-help in this form of situation is normally counterproductive. Seek counsel.