How and at what age does a teenager become independent of their parents?

EIGHTEENyou are an adult at 18.

In every state, someone under the age of 18 is considered to be a minor and therefore under the control/authority of their parents. The laws regarding emancipation vary by state. Some states (about 1/2 of them) allow a minor to petition the court for a declaration of early emancipation. In the states that do not allow that, 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 allow a minor to request early emancipation: generally, you petition the court for a declaration of emancipation. Most states require that you be at least 16 before you can do that. Among other things, 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, especially if your parents object. The courts generally don't like to override the authority of parents, so you would have really prove your case. Just not getting along with your parents is not enough of a reason. There has to be a legitimate reason that it would be better for you to live on your own. The courts then decide rather to grant or deny your petition. It is not a quick and easy process.