i spoke to someone that told me it was 18 dollars a day but if i made a reservation it would be 13 it had a terminal in it & the train leaves every10 minutes can quide me as to how to make the reservation

Sounds like you're in the actual JFK Long Term Parking lot, make the reservation and print the confirmation. Follow the directions on the confirmation, you pay when you leave the lot. You can pay with cash, credit/debit card, or EZPass

Yes reservation helps you park nearby train stations