How can a 15 or 16 year old emancipate himself from his parents in the state of New Jersey?

Out-of-court settlement is the easiest option if it is possible; your parents may consent, which would take care of it. If they don't, then you can ask a judge to emancipate you; ideally, you would obtain the help of a lawyer in presenting this application, although I don't know if you can afford such a thing, just as I don't know your reasons for seeking emancipation. If you can show that your parents are abusing you in some legally significant manner (if they are endangering your health or stealing your money, for example) the courts should be sympathetic to your request. If it's just a matter of some dispute, over how late you can stay out, and so forth, the courts will be less sympathetic.