How does someone get the correct forms and paper work to start the emancipation process?

Does that someone have a good job and can support himself? Does he have a place to live?

Someone contacts the court and asks how it is done in their state.

Not all states in the U.S have emancipation status.
The link below gives you an overview,
Emancipation in the United States Fact Sheet at Juvenile Law Center (http://www.jlc.org/factsheets/emancipationus/)