The Shadowreign is the set of areas in the "Wings of the Goddess" expansion of Final Fantasy XI, so, to unlock it, you must first purchase "Wings of the Goddess".
After purchase and activation, you will want to go to one of the three areas surrounding Jeuno (Rolanberry Fields, Sauromogue Champaign, or Batallia Downs) and look for a "Cavernous Maw". You'll probably find it easier in Rolanberry or Batallia. Go through it, and you will enter one of the three corresponding areas in the Shadowreign.
Your first task is a long and arduous run through the Shadowreign to get to one of the three major cities in the past. But that's another question.