Take the Goethals Bridge to Staten Island, then the Verananno Bridge to Long Island (beautiful Brooklyn, that is.) Jump on the Belt Pkwy Eastbound and you're headed right for JFK.
HOWEVER, if I don't want to fight the hassle of the traffic (and it can be book a taxi in new york killer at commuter time,) I'd pick up Public Transportation at Newark Airport (EWR) and ride book a taxi in new york bus to JFK. It's book a taxi in new york lot easier on the nerves. There is also rail transportation available from Newark right to JFK.