In most instances, you can wait until your scheduled appearance before making the request for a court-appointed attorney. I recommend you make a call to the Family Court and specifically ask the Clerk if there is anything you can and should do in advance of the scheduled appearance.
Mr. Rosen practices matrimonial and family law in Great Neck, NY. His response here is not legal advice and does not create an attorney/client relationship. The response is in the form of legal education and is intended to provide general information about the matter in question. Many times the questioner may leave out details which would make the reply unsuitable. You are strongly advised to confer with an attorney in your own state to acquire more information suited to your particular circumstances.
The first answer is not the best way to go unless you're looking to make multiple appearances at Family Court. There is paperwork available to seek court appointed counsel. You should obtain it, fill it out and submit it as soon as possible. Otherwise on your first appearance you'll find yourself with an adjournment and a reschedule date.