You can pay by direct debit, credit card, or send in a check with their payment voucher. See the following for payments options from your State.
https://www.tax.ny.gov/pay/ind/pay-income-tax-online.htm
If you want to mail in a check after you e-file, you would send the check along with IT-201 payment voucher.
https://www.tax.ny.gov/pdf/current_forms/it/it201v_fill_in.pdf
