Mentor Guide:
You can offer another character to be their Mentor by opening the Friend Manager and pressing the + button in the Mentorship tab.
For example, after becoming a Mentor in the Mentorship tab you can choose characters that would be your Mentees.
Not every character can become a Mentor or a Mentee. A character can only become a Mentor if they had already gone through Awakening and reached Lv. 105. A potential Mentee can't be higher that Lv.104.
After a Mentee finishes their Mentor can't take on new Mentees for a day. After discontinuing Mentorship for some other reason, a Mentor can't take on new Mentees for two days.