Sojourn,
On your arrival at JFK take the airtrain to Jamaica Station (in Queens). Catch the Long Island Railroad to Penn Station Manhattan. At Penn Station catch a Amtrak train to Wilmington. It should take you about a hour to get to Penn Station and the Amtrak train takes another hour and 25 minutes to Delaware. Check Amtrak for schedule of trains to Wilmington, Delaware.
reply to sojourn0901