the cheapest way to go is the air train from jfk to the A train and then transfer onto 4,5,6 at Atlantic avenue.
Edit: Heres another and maybe a quicker option (i found this on yahoo answers)
Step 1: take the Airtrain from the terminal to Jamaica Station. Make sure you listen for the announcement "Station D: Jamaica Station. The fare for the Airtrain is $5, which you pay when exit the Airtrain system at Jamaica Station.
Step 2: at Jamaica Station, transfer to the Long Island Railroad (LIRR). Take any eastbound train from Jamaica Station to Penn Station. The fare is $7.25 one way peak/$5.25 one way off peak. If you're taking the LIRR on the weekends, the fare is $3.25 one way.
Step 3: at Penn Station, transfer to the New York City Subway. Take the uptown (northbound) #1, 2 or 3 subway lines (Red Line on the subway map) from Penn Station to Times Square.
Step 4: at Times Square, transfer upstairs to the 42nd Street Shuttle (Black Line). Take the Shuttle from Times Square to Grand Central.
Step 5: at Grand Central, exit the subway into the Grand Central Terminal.
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