Take the AirTrain from JFK to Jamaica Station on the Long Island Railroad (LIRR)($5). Then take the LIRR all the way to Ronkomkoma station (last stop, about an hour, $15?). Then you can take a taxi from the Ronkonkoma station to MacArthur. I think it's something like 10 or 20 bucks.
Take the AirTrain from JFK