there are three ways that i know of to get to the airport...
1. the subway which means lugging your bag up and down the stairs of the platform and then switching to the airtrain at jfk total cost is about $7
2. Taxi depending on what time of day your are going to the airport it cost cost anywhere from $40 and up
3. take a cab from penn station to grand central and take the charter bus that is across the street from grand central to the airport. if you google it you will find the information with time and cost of the bus. ive used this bus a number of times and its always worked out well.
JFK Airport Guide
bus