In New York the subway is refered to as "train". Many people see it as the way to move across Manhattan. Be sure to take the subway at least once on your New York City Trip, if only for the experience. The "stand clear from the closing doors please", that sound of the train entering the station, the musicians. It's just like in the movies. With you in it! Be prepared for lots of people, not so clean trainstops and subway cars that feel like a sauna in the summer ...
Check the MTA Subway Map to plan your trip. With 468 stops in 24 different routes and services identified with numbers, letters and different colors it's easy to make a mistake. Remember: the Uptown and Queens bound trains go North / the Downtown and Brooklyn bound trains run South. Black dots on the map refer to "local trains" that service every station. The white dots refer to the "express trains", they only stop at a couple of stations along the route. There's no need to look for a timetable. Generally a train goes by every couple of minutes.
The larger subwaystations will have a ticketbooth where you can buy tickets, ask questions and get (free) subwaymaps. It's also a good idea to download a NYC subway app so you'll always have the map at hand. Each subway car has a map which shows you where the train stops and usually the (next) stops are also announced.
Get your ticket at a ticketbooth or a machine. For each new metrocard you buy you have to pay $1. You have different options: "Pay-per-Ride" (which can be refilled) and Unlimited Ride cards (7 or 30 days). A refill of $ 5,50 or more will get you an 11% bonus. Depending on the number of rides you'll make, the magical amounts to put on your card are $ 22,30 or $ 27,25. With the 11% bonus this is enough credit for 9 or 11 rides without keeping an (unusable) balance on your card. Using the card is simple. Just swipe it (with the magnet towards you) and the turnstile will open. Every time you swipe the card, $ 2,75 is taken off your balance.
There's usually not much going on in the train. People are staring into nothingness, listening to music, reading a book or playing with their phones. It can get very crowded and if you can't find a seat, hold on to something. New Yorkers usually don't appreciate it if you fall in their lap.
Maybe you'll also want to check out Milo Beckhem's explanation on how to use the subway in Manhattan.
Whatever you do, do not get into an empty car. If an empty car glides into the station, it’s probably too good to be true. It is probably empty for a reason, such as a foul smell or badly functioning air-conditioning system. The rule of thumb? Stick with the crowds. Cars that are more packed can be too close for comfort, but hundreds of riders can’t be wrong.