Go out to the street to hail a cab. Unlike most every other city in the United States, you rarely can call and prearrange a pickup in New York City. With that in mind, you need to hail a cab by waiting on sidewalk until you see a cab. Most every moderately busy street in New York City has a multitude of cabs.
Learn which cabs to hail. When viewing the cabs that are driving by, notice the lights atop the cab. When the middle light is lit, that means that the cab is available. If all the lights are lit, that means that cab is off duty. If none of the lights are lit, that means that the cab is in use by customers. If you are new to New York City, check out the different cabs for a few minutes until you can recognize the difference between an available cab, an off-duty cab and an unavailable cab.
Hail a cab by sticking out your arm while you step off the curb. That is the sign that you want the cab to pick you up. Sometimes even an available cab won't see you and can pass you up. If that's the case, just keep trying until you get a cab to stop. Sometimes it may take a couple attempts before you are able to successfully hail a cab.
Know the rules and regulations about traveling by taxi cab. A cab can have a maximum of 4 passengers. However, small children who can sit on a passenger's lap don't count toward the 4-passenger limit.
Carry enough cash to pay for the cab as it's the universal--and only--way to pay for cabs in New York City.