New York City is served by one emergency service that handles all kind of emergencies, police, fire and medical. To access this service you have to dial 911 from your landline or your cell phone. No matter what the emergency you must try to remain as calm as possible while dialing 911 for once you dial this hotline the personnel who man this service will ask you about the nature of the emergency and then ask for your address in order to dispatch the appropriate service and also to verify the location of the call.
For this you need to know how to describe your street address (if you are based in Manhattan this will probably consist of an avenue and a cross street). Once you have described the emergency and the address the dispatcher will then dispatch the appropriate service to help you. If you are calling about a major incident you have to bear in mind that there may be several other calls of the same nature and you may be put in queue.
Apart from the 911 emergency services, New York City is also served by a non–emergency hot line, 311 (http://www.ci.nyc.ny.us/apps/311/) which provided information about several services offered in the city.
Phone numbers of various police precincts and other important city hotlines like the terrorism hotline can be found at (http://www.nyc.gov/html/nypd/html/home/contact_information.shtml).