Take the AirTrain to Jamaica, then hop on the E to Manhattan (should be express at this time of day). Get off at Lexington Avenue and transfer to the downtown #6 train. Take the 6 one stop to Grand Central and you're right there.
If the weather is nice and you don't have a lot of luggage, you could even walk from the E at 53rd and Lexington down 11 blocks to Grand Central and avoid the transfer to the 6. It's a somewhat long walk through the tunnels from the E to the 6, so walking from 53rd wouldn't take that much more time than the subway transfer.