If you don't have your own car, take the air train to Jamaica Station then the E to the 1,2,3,or the f going to Hudson yard
The easiest way to port authority from jfk is to get a ride from someone or a taxi 🚕 , but if you're trying to save money and get there more economically you could take the AirTrain from your arrival terminal ( terminals 1, 2, 4, 5, 6, 7, or 8) to either Jamaica ave or Howard Beach stations both where you transfer to the MTA transit which takes you to manhattan. Note that the AirTrain is free to ride throughout the airport and both to and from both Jamaica ave and Howard Beach stations but you will have to purchase a metro card Which is $7 plus $2 to transfer to the mta transit. Get the A train from Howard Beach station which puts u close to port authority in manhattan The E and J train is from Jamaica ave. Note either station you choose to go to please follow the map and signs or ask a transit worker for help if needed
The best way to get from Port Authority Bus Terminal to New York JFK Airport (JFK) is to train which takes 45 min and costs $13 - $16. Alternatively, you can bus, which costs $19 - $27 and takes 1h 50m. (https://www.rome2rio.com/s/Port-Authority-Bus-Terminal/New-York-JFK-Airport-JFK#:~:text=Airport%20(JFK)%3F-,The%20best%20way%20to%20get%20from%20Port%20Authority%20Bus%20Terminal,%2427%20and%20takes%201h%2050m.)
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