How do I receive the Celestian Awakening quest?
As usual in this game: talk to the bartender. As soon as it's time for this quest, rumors will hint to you. And also read the characters' phrases, two characters in Agranor will tell you when the time comes.
If you meant to teach Celica to awaken the image hidden in her body, then it is a bit of a routine task: you need to meditate for several days, following the ritual indicated by the girl with tails. And when a friend appears, you need to trust her...