Getting There

Since I don't know where you are coming from, about the only thing I can do is give you some tips...

Flying in

If you are flying in, there are three major airports that service New York City: John F. Kennedy, Laguardia and Newark, NJ. The taxis have a set fare from JFK, which was $30.00 to anywhere in Manhattan, but has probably gone up. However, that is not the case with Newark, and I do not know about Laguardia, so you're probably better off to take a shuttle service into the city. I don't know much more than that because I have never flown into New York.

The train

From most of the country you have little choice = Amtrak. However, from Connecticut, there is also Metro North, which also services parts of New York state north of NYC. There must be some commuter trains from other areas, but I do not currently have information about them.
I used to go to New Haven, CT, and take the train from there. Metro North goes as far as New Haven, and there is a service called Shoreline East that you could take from other towns along Connecticut's southern coast and then connect with a Metro North train in New Haven.
From New Haven you still have the choice of Metro North or Amtrak. Metro North goes to Grand Central Terminal and Amtrak goes to Penn Station. In most cases, it will not matter much which train station you end up in, although I have heard that Penn Station has a problem with pick-pockets. Why this would be more of a problem there than at Grand Central, I don't know.
The main differences between Amtrak and Metro North are:

1. The seats on Amtrak are like those on a charter bus, the ones on Metro North are more like those on a school bus.
2. Amtrak is about twice as expensive as Metro North.
3. Because it is a commuter line, Metro North has more trains going and coming, so it is more flexible than Amtrak as far as when you can get there.

Another difference between them is pointed out by the names of the train stations.
Grand Central Terminal is just that, a terminal, the end of the line. When a train pulls in, there is a wall in front of it. When it leaves, it goes back the way it came. That is why it is good for commuter lines, as they usually go back and forth between two end points.
Pennsylvania Station is a station, a stop on the way. A train pulls in, passengers get off and others get on, and then it continues on its way in the same direction it was travelling when it pulled in.

Oh, yeah, if you are looking for Grand Central Station, there is such a place, but it is the subway station at Grand Central Terminal. These are easily confused, and it is not really that important. If you ask a taxi driver to bring you to Grand Central Station, for example, you will get to the right place.

Driving

I have driven into the city several times recently, and it is not as bad as I once thought it would be. There are many tunnels and bridges into the city. The best bet would be to use an online mapping service or a GPS to get driving directions. Get the directions to a specific address in the city, and there should be a place to park nearby.
One of the biggest problems would be the cost of parking, or finding a good place to park. Most of the parking garages and lots are valet parking, where you have to turn over your keys to an attendant. If you want to park yourself, there is only one place that I know of, although there are probably others. It is on 42nd Street around 9th Avenue.