Unlike the Dark Knight, unlocking the Astrologian in Final Fantasy XIV: Heavensward is fairly straight forward. Marked on your map in the Pillars is the Athenaeum Astrologicum. Enter it and you’ll find Jannequinard, your quest giver. Accept the job quest, Stairway to the Heavens, and follow its instructions.
First, you’ll have to speak to three Astrologians right outside of Athenaeum Astrologicum. Easy. Next, teleport to Coerthas and head south to reach the Observatorium. Go about half way up the large tower and you’ll find your next quest target. He will point you in the direction of Quarrymill which will be your final destination.
Follow your map marker and you’ll view the final cutscene. After that, you’ll have unlocked FFXIV’s newest job, hurrah! However, you’re going to have to learn how to be a proper FFXIV healer real fast, because your next quest will rely on your ability to keep a small party alive.
While you’re free to do what you like after unlocking Astrologian in FFXIV, it’s highly recommended that you go ahead and also start your next quest right away from Mace’s Granddaughter.