How can I go to JFK Airport from the Greyhound station in Manhattan by using the subway? What are the subway stations called at the Greyhound station in Manhattan and at JFK Airport?
When you arrive on Greyhound in NYC, you will be in one of the underground levels of the Port Authority bus terminal. From here, take the escalators one level up to the subway level. The lower level is somewhat sloped; the escalators you want are uphill at the far (highest) end of the level. On the subway level you can purchase a MetroCard to pay your subway and AirTrain fares, if you don't already have one, or top one up if you do. Then enter the subway system.
At the Port Authority subway station, you will take the E train toward Jamaica Center ($2.75), and exit at the next-to-last stop, Sutphin Blvd/Archer Av.
At Sutphin Blvd/Archer Av, you will change to the Jamaica AirTrain ($5) to JFK Airport. Follow the overhead signs to the JFK AirTrain. The AirTrain stops at all terminals; exit the train at your departure terminal.
If you can't afford, or don't want to pay the $5 for the Air Train, you can take the 'A' train from the port authority stop to Lefferts Boulevard. Get on a Downtown/Brooklyn Bound A train.
Once there, you can take a Q10 bus. You can see this bus on the subway map. There are other buses too.
Keep in mind that while this will save you only a dollar or two, it might take a little longer. But if you have a long wait between the bus and flight, and time to kill, this is a good option.
Alternatively, last time I tried (5+ years ago), it was possible to walk from the Howard Beach stop to the terminal. Edit: Comments mention that this has been mentioned in another SE Travel Post. Thanks!