Take NYAS express bus from terminal, or Airtrain from terminal to Jamaica Station and then either LIRR or E subway to Penn Station. At Penn Station you can take Amtrak Northeast Regional or Acela (more expensive but faster) train to DC, or on street level you can take the Megabus, Vamoose Bus or Bolt Bus to DC. Bus is much cheaper than train.
Take NYAS express bus from