Airtrain and City Trains/Subway
The most affordable means is a combination of the Airtrain system and the metro trains that run into the city. The airtrain runs 24/7, but check for construction delays in summertime. The airtrain connects all airport terminals together and runs to Howard Beach Station where one can get the A Train to Brooklyn and Lower Manhattan, and Jamaica Station to get the E Train and the Long Island Railroad LIRR to Queens and Lower Manhattan and Penn Station.
The total time to Manhattan using the subway method takes 60 minutes. Going out to the airport on the “A” train, make sure the destination signs read Far Rockaway or Rockaway Park. Trains to Lefferts Blvd. do not connect to the airport! If you board the wrong train, transfer at any station at or before Rockaway Blvd. If you forget and overshoot, go to the end of the line and either backtrack or take the Q10 bus directly to the airport. The biggest thing to be aware of is that peak times will bring added wait time to a journey and so it is always good to plan on traveling with plenty of time.
The New York Bus services provides services to/from Grand Central Terminal and the Port Authority Bus Terminal for $16 one-way, $29 round-trip (return ticket). Buses depart every 15-30 min and the trip to Grand Central Terminal can take up to 90 min. While the online schedule shows stops at Penn Station, the bus does not go there 12:00-18:00; however, SuperShuttle offers a free connecting service between Penn Station and Grand Central Terminal.
The most direct into the city from JFK is in a taxi, wait times can be long depending on the time of day. General expectations show that fares are around $55 into Manhattan, this does not include tolls which can be another 6 dollars. Taxis to points other than Manhattan and taxis to the airport from anywhere use the meter. Always takes rides from real companies with proper ID and licensing and know that oftentimes with traffic the public transit routes can take the same amount of time or even be faster.