If you use the Shoreliner East (closest free lot is in Old Saybrook, exit 68 off 95. CT is does NOT use mile based exit on 95 yet), you have to change trains New Haven to the Metro North system. That will get you into NYC at Grand Central Station and from there you can access the Subway system or catch an uber/lyft/taxi to your end destination. Use the Trip Planner to remove the pain of figuring out which train you need to get on when the transfer happens for both outbound and inbound trips.

If you're using Amtrak- it'll drop you at Penn Central Station, which also has easy access to the subway but is nowhere near Grand Central. The earlier you get your tickets/closer to NYC- the cheaper they'll be.