How do I start the emancipation process?

This is a matter for Court, but the process varies in each County.  There are certain findings that need to be made.  These may be contained in County forms.  The suggestion is to either contact an agency, if there is one in your County, or an attorney to lead the way through this process to insure it is done both quickly and correctly.  If you need an attorney, one may be obtained via the County Bar local referral program.  You can start there or, maybe, the County Clerk can give you the needed forms or they may be obtained from the County Law Libary.  Since this is a process that carries certain risks and responsibilities, it may be wise to get some counsel before proceeding to Court.  This is another reason to seek out an expert.