Empire: You talk to a member (Not Bloodoath or Citizen) of the sect you want to get into, and have them bloodoath you.
Village: Not sure about the new way to appy, but I guess it can easily be anwered by talking to a villager. Something automated for becoming Village App though.. i think.
The rest in most cases require a short note stating your interest in joining. Then you have to seek out the leader, and in some cases he will ask for recommandations from the current members.
Scion is not advisable for a newbie! Its a hard cabal to be in, since nearly everyone is your enemy. A newbie would not survive it.