Easiest way into Manhattan is to take the JFK light rail from the terminal to Jamaica Station. From Jamaica Station, transfer to either the Long Island Rail Road (LIRR), or the subway (there is only one line). LIRR will take you to Penn Station, midtown on the East side at 34th St. and is planned in the near future to go to Grand Central Station on 42nd St.
Subway will allow you to transfer to all the other subway lines, so the destinations are all over NYC. Time is about an hour for the whole trip.
LIRR is more expensive than the subway, but more comfortable and faster.
If you get lost or need help don’t be afraid to ask. NYers are friendlier than they seem