Are you coming from CT or MA? Your lead statement is a bit confusing. As Don says you would use Amtrak from MA to NY Penn Station.
From stations in eastern CT as far as New Haven (and certain points west - see MetroNorth map link below)) you can use MetroNorth's New Haven line to Grand Central Terminal (E42nd St & Park Av)
Metro North map http://web.mta.info/mnr/html/mnrmap.htm
New Haven Line timetables: http://web.mta.info/mnr/html/planning/sc...
For other areas in CT not served by MetroNorth you would have to check with Amtrak for their nearest station to you in CT. Amtrak goes to NY Penn Station (W33rd St between 7th & 8th Avenues.
If you will be arriving in NY at Penn Station - use the NYC Subway - Uptown C train for stations along Central Park West (American Museum of Natural History is at the 81st Station on the C train. If you just want to walk around the west side of Central Park take the uptown A or C to 59th St-Columbus Circle station. For the Museum of Modern Art (W53rd St between 5th & 6th Avenues take an uptown E train to 5th Avenue-53rd Street station (use stairs at back of the 5th Av-53rd St station to exit).
If you want the eastern side of Central Park (along 5th Avenue) - from Penn Station - take an uptown 1, 2 or 3 train one stop to Times Square. Transfer to an uptown N, R or W train if you want to go to the Central Park Zoo (5th Avenue station - exit at the 60th Street end) and enter the park around E61st Street & 5th Avenue.
If you want museums on the east side of Manhattan (Metropolitan Museum of Art, Guggenheim Museum, Museum of the City of NY) from Penn Station take the uptown 1, 2, or 3 train to Times Square and then transfer to the 42nd Street Shuttle (S train) to Grand Central. At Grand Central transfer to the uptown 4, 5 or 6 train to 86th Street Station (for the Metropolitan Museum of Art or Guggenheim) or 10rd St (6 train only) for Museum of the City of NY.
Rather than trying to list all options since I can only guess whether you are coming in via Amtrak or MetroNorth, I have provided a link to the NYC Subway Map below.
NYC Subway Map (can be downloaded (PDF file) http://web.mta.info/maps/submap.html
If you have specific questions, please post them here (New York City forum). As you can see there are people here who are willing to answer your questions.
Enjoy your visit.