Taxi ranks are on the arrivals level of every terminal. Taxis from the airport to Manhattan have a flat rate of $52, which increases to $56.50 during peak hours. Taxis can be reserved from inside the airport, or can be hailed at a taxi rank. See JFK Airport's estimated taxi fares here.
Uber, Lyft and Via are ride-sharing apps available to use in JFK Airport. To use any of them, download the app, fill in the personal details required, and enter the pickup location (the terminal and door number). The apps provide a fare estimate before confirming the ride.
Limousine and Helicopter:
Limousines and helicopters can be hired to leave JFK Airport and it is best to book them in advance. The JFK Airport website suggests Connecticut Limo as an authorized service, and the highest rated New York helicopter service is New York Helicopter. Limousines will generally pick up passengers from the arrivals area, but it is recommended to confer with the companies about their pickup policies before traveling. Prices will vary for each company.