How can a 16 year-old become emancipated?

In Arkansas emancipation is known as "the order of removal of disabilities" and an individual must be at least 16-years-old for it to be granted.  Additionally, it will require a court order and may be limited in scope.  I'm not at all certain, based on your facts, that it will be available to your friend.

Making application to the court for a guardianship might be a better legal avenue to pursue.  However, that is also not easily accomplished.

What you should all do now is to consult with an attorney in your area on the best way to proceed with this.  If money is an issue, see if your friend qualifies for representation by Legal Aid or see if they can recommend someone to help.  Also, check if there is a law school nearby to where you live; they typically run free/low cost clinics that handle these type cases.  Additionally, you can contact the local Bar Association in your county; they may have a list of attorneys who will take the case "pro bono" (for free) or at least for a reduced fee based on income/circumstances. 

Best of luck.