Funny you should ask, because I was just looking that up myself. Google LGA airport, and look for "Connection between airports", and you'll see a list of options to get from JFK<->LGA<->EWR. Among from LGA and EWR, you can do the Subway, and then AirTrain route, or the NY Airport service express bus, cost about 15, or the Olympia route the other mentioned, cost about 12. I think the buses takes about an hour or so, i think it's the best way to go, rather than hauling your luggage all over the subway tunnels.
Good luck.