Travelling from JFK to Jersey City

First, no options are particularly fast, but...

A) Take the AirTrain to Jamaica Station.

B) Take the E Train to World Trade Center

-or-

A) Take the AirTrain to Howard Beach

B) Take the A Train to Chambers Street

-then-

C) Exit at Vesey Street and walk one block West to World Trade Center PATH station. Shortest. -or- Follow the tunnels to Fulton Center and cross to the World Trade Center PATH station. Underground. I think there's still construction going on.

D) Take PATH to Exchange Place

E) Take the Hudson-Bergen Light Rail south.

Another option:

1. AirTrain to Jamaica Station

2. Long Island Rail Road to Penn Station

3. Walk one block to 33rd St PATH

4. Take PATH to Hoboken

5. Connect to Hudson-Bergen light rail

This would be a bit more expensive than Johns-305's answer, but could be a little faster since LIRR is generally quicker than subway.

You could take a taxi from JFK to a PATH station in Manhattan but you might as well just take the JFK AirTrain to Jamaica and get the Long Island Rail Road into Penn Station as it is the fastest and most economical way to get into NYC. You'd then be one block from the 33rd Street PATH station.