Track down Proctor Ingram near the power armor stations. Optionally, she can be persuaded to reveal how she lost her legs.
Track down Proctor Teagan, who is stationed in the Prydwen armory near the power armor stations. Speaking with him reveals that he has some work available for the Sole Survivor after the completion of this quest.
Track down Proctor Quinlan within as office near the mess hall, in which, just as Teagan had done, will offer work for the Sole Survivor after the completion of this quest.
Track down Knight-Captain Cade within his medical office right across from Quinlan's office, and take his medical exam. He can be returned to later to receive medical services.
Meet Knight-Captain Cade
In order to become an effective part of the Brotherhood, Elder Maxson has ordered me to tour the Prydwen and familiarize myself with her crew.