There are several trains running daily into and out of New York City. They stop at Grand Central Station, Union Station and a number of other smaller stations en route. You can park your car at a train station well outside the city limits for a small fee, and buy a ticket into the city to avoid the hassle of driving in and parking yourself. With the price of parking meters these days, it's probably no more expensive and a lot less of a headache.
If you're just outside the city limits or in another burrough, you can easily take a bus to your destination. Public transportation in New York City is easy to use and makes frequent stops. The cost is low and payable with a Metro Card.
New York City has dozens of underground routes to take you anywhere you need to go. If you're in one of the burroughs, you can head underground and take the downtown line. Be sure to have a subway map handy if you are unfamiliar with the area. The subways run by color and letter.