Originally Posted by Blumie

Three hours will be plenty. When you get off your flight, you'll have to clear immigration, then claim your checked luggage, and then clear customs. Immediately after you exit customs, you will be able to recheck your checked luggage in Terminal 7. (When you exit customs, turn right for the baggage recheck desk.) Then follow the signs for the AirTrain and, instead of taking the train that goes to all terminals, take a train going either to Jamaica Station or Howard Beach Station. Terminal 8 should be the next stop on the train.

(The "all terminals" train also will get you to Terminal 8, but it runs in the opposite direction, so Terminal 8 will be the last stop instead of the first. On occasion, the Jamaica and Howard Beach trains run in the wrong direction, too, so if you get on either and the first stop is Terminal 5 rather than Terminal 8, get off and switch to an "all terminals" train.)

In any event, if your inbound flight arrives on time, you should have plenty of time for the connection, even if you encounter long lines at immigration or reclearing security at Terminal 8.