Easiest is the shuttle bus, which is $50 one-way and will pick you up and drop you at your door in New Haven.
Cheapest is to take Metro North into the city to Fordham Rd, then get the D subway to the A to JFK. Maybe $13 on Metro-North, $2.25 + $5. It's a little more expensive to take Metro-North all the way to Grand Central. You can also get a bus directly from there, about $20, or take the 4 and transfer to the A at Park Place, downtown. You can get to NYC from New Haven on Metro North for well under $25.
Easiest is the shuttle bus,