Phone numbers within the US consist of a three-digit area code followed by a seven-digit local number. In NYC, you will always dial ten numbers: 1 + the three-digit area code + the seven-digit number. To make an international call from NYC, call 011 + country code + area code + number. When calling Canada, there is no need to use the 011.
No matter where you’re calling within New York City, even if it’s just across the street in the same area code, you must always dial 1 + the area code first.
Manhattan 212, 646, 332
Outer boroughs 347, 718, 929
All boroughs (usually cell phones) 917
International travelers can use local SIM cards in a smartphone provided it is unlocked. Alternatively, you can buy a cheap US phone and load it up with prepaid minutes.
If buying a US SIM card, you'll want to go with either AT&T or T-Mobile (or companies using their networks) as these carriers run on the GSM network, the standard used in most other countries. You may be able to preorder a card at home, or you can simply purchase one from the relevant carrier's store in New York.
If purchasing a cheap US phone, you can also look into Verizon and Sprint, which use the CDMA network. Phones can be bought in telecom stores, drugstores, grocery stores and big retailers like Target.
If you plan on traveling outside of NYC, make sure you are using AT&T or Verizon – these two carriers have the best coverage in more rural areas.
Data coverage in NYC is LTE.