The best way to do it is to get your marriage certificate BEFORE your chasunah. Your mesader kedushin will sign it and mail it in after the chupah. If you neglected to do so, you may go get your marriage certificate by googling “NY marriage certificate” or any state you live in and follow the instructions. It is always easier and faster to get it in the suburbs than in the city. Take it to your Rav with your kesubah and he will handle it for you.
BTW, Rav Moshe Feinstein Z”L was very adamant about getting a marriage certificate before the chupah. He liked to do things by the book.