From Grand Central there is a NYAS express bus to JFK. You can also take the uptown #6 subway one stop to 51st St. and transfer to the E subway to Sutphin Blvd./JFK. Then take Airtrain to from there to your terminal. If you decide to go to Penn Station the LIRR will take you to Jamaica Station and the Airtrain as above.
From Grand Central there is