Or you can take the Long Island Railroad (LIRR) from Penn station to Jamaica. Travel time about 20 minutes.If you travel on the weekend, buy a "City Ticket" for $3.25.
If you take the A subway from Penn, travel time can be 45-60 minutes. If you take the A subway, be sure to take the one marked "Far Rockaway" or "Rockaway Park". DO NOT TAKE THE ONE marked "Lefferts Boulevard". Both subways share the same track and they alternate between Lefferts and Rockaway.
After getting on the "Rockaway" subway, be sure to get off at the "Howard Beach" station. Follow the signs for the Airtrain. Note Airtrain is $5. You eeed to purchase a "Metrocard" from the special vending machines. There are plenty of customer service people to help you out.
Penn to JFK