It depends on how long you have between flights. It is probably about $100 to take a cab to Newark. You can also check rates with some of the car service companies to see if they are any better. Check www.telacar.com.
In terms of public transportation try this: http://gonyc.about.com/gi/dynamic/offsite.htm?zi=1/XJ&sdn=gonyc&cdn=travel&tm=19&gps=258_640_1020_568&f=10&su=p284.9.336.ip_p531.50.336.ip_&tt=2&bt=1&bts=1&st=38&zu=http%3A//www.nyairportservice.com/ . Anything else and it will be about a three hour tour on NYC public transportation. You can do it, but you will have to take the Airtrain to the A/C/E train to Penn Station, and then take the regional NJ Transit rail service to Newark Airport. All in all, it will be a waste of time and probably more expensive.
Good luck.
Getting to Newark Airport from JFK