No, you cannot take the subway to Greenwich from New York City. But you can take the subway to the MetroNorth stations, and then take MetroNorth Railroad to Greenwich.

See the Related Link below for MetroNorth schedules and fares. You will need to click the icon on the RIGHT, the one that says "Click for lines EAST of Hudson - Harlem, Hudson, New Haven."

MetroNorth trains depart from Grand Central Station, and from East 125th Street and Park Avenue. Take the 4-5-6 subway line (the dark green line) to either 42nd Street (Grand Central) or 125th Street, and then transfer to MetroNorth.

See the second Related Link for a complete New York City subway map.

There is no train that runs directly between Penn Station and Grand Central. You have to take the subway: the Uptown 1-2-3(the red line), 1 stop, from 34th Street-Penn Station to 42nd Street-Times Square, then transfer to the S shuttle train (color grey) to 42nd Street-Grand Central.

Trains on the New York City subway system operate continuously. There are schedules you can download, but they're often inaccurate.