If you prepared your New York State tax return in TurboTax the program should have prompted, you to print out a copy of your State return. Included in that print out should be filing instructions along with a payment voucher. If you did not set up a direct payment plan while completing your New York State tax return in TurboTax,you can pay your taxes owed by mail or electronically.
To pay your taxes electronically you can do so at the New York State Department of Taxation. This secure online application allows you to pay by either debit card, ACH, credit card or check/money order.