The laws vary by state, and not all states have emancipation laws. In the states without emancipation laws, the only way to become emancipated is by (1) turning 18 (2) getting (legally) married (3) joining the military (which minors have to have parental consent to do). In the states that do have emancipation laws: generally, you petition the court for a declaration of emancipation. You have to prove that you are capable of supporting yourself (and that means of support can not be public assistance). You also have to prove that it's in your best interest to be emancipated. That's not always an easy thing to do. The courts generally don't like to override the authority of parents, so you would have really prove your case. The courts then decide rather to grant or deny your petition. It is not a quick and easy process.
I was emancipated and I didn't think it was that hard, I did have a good reason for wanting to be emancipated, i was physically abused by a sibling, I went to the court house and asked a few ?'s and they were very helpful, on my court day I had pictures of bruises and proof that I had a job, was still in school and had found a safe and stable resident, it will help if you bring whom ever you are staying with to verify what you say and to let the court know that you can countinue living there.
I took my daughter with me in New York to get emancipated. She was married, had a baby, and was working getting 8.25/hour. It was rather easy, she was willing to request for this emancipation. You must prove that partied are in agreement for tihs and it is in the intersest of the child to get this done and hopefully they will fly away.