Who knows commuter trains in New York area?

If you really wanted to take *commuter* trains, you could take SEPTA from Newark into Philly, change for the SEPTA train to Trenton, switch at Trenton to NJTransit, and ride that to Penn Station NYC. Obviously, that would take a long time and not be much fun. the easier method is Amtrak from Newark to Penn.

From Penn Station you can either take the Long Island Railroad (about $7 each way, depending on time of day) or the E subway ($2 each way) to Jamaica train station in Queens, and from there the AirTrain monorail ($5) to JFK terminals.

Take Amtrak from Dover, De. to Penn Station NYC.

At Penn Station you will have a choice.

You can take a cab to JFK - $45 flat fee or take the subway and airtrain.

If you choose the subway and airtrain.

From Penn Station get on a Queens bound E train. Take it to the 2nd to last stop - Sutphin Blvd - Archer Ave station. There you can pick up the Airtrain to JFK.

Amtrak has only two stations in Delaware, a major one in Wilmington and a smaller one in Newark. There are no Amtrak stations anywhere near Dover, unfortunately.