Your best and easiest way to travel from JFK is by taking a bus (airporter, airport express) to Grand Central station. It shouldn't cost you more than 15.00. THey might even have a special. Recently I got a ride from LaGuardia on the bus to Grand Central for $5.00! From Grand Central you can then take the Metro North New Haven Line to Stamford. It's a 50-minute ride and costs about 10.00 off peak.
train from JFK to Stamford, CT