Setting
Not much is revealed of the Erudite initiation, but from the manifesto, they most likely study, and take rigorous tests. It is also stated by Therese that there is an initiation intelligence test that, if not passed, results in one becoming factionless. Caleb reveals that each of the initiates selects and is trained in a certain subject of expertise in Erudite.
http://divergent.wikia.com/wiki/Erudite