The commonest tropes in depictions of medieval times--the times that so much of D&D is meant to emulate--are in the roles played by people in society. There is so often a King or Queen, a Lord or Lady, a Duke or a Duchess, to lead. Thanks to the fantastical additions to the game which are meant to represent Tolkien's fantasy world from The Lord of the Rings and The Hobbit, one of the most common roles we think of is the wizard. There are knights and peasants, a court jester, perhaps, and likely a mystic of some sort. It's this mystic role that I want to address here: how to create mystic characters and create mystic experiences for your players.
One thing to address from the start: we need to determine what way you want to portray mysticism. For story reasons or personal preference, you may need or want to portray a mystic character as trustworthy or not, as legitimate or not, and as reasonable or not. Knowing your intentions before you start can allow you to make the best choices for your situation.
And a last note before getting into it: I am myself something of a diviner. I have read tarot cards for over 1 decade, sometimes professionally, but mostly for free because I do think it can help people. I study other witchcrafts, and while I'm not going to go into the full extent of it, I think most anyone would consider me pretty well in the mystic camp. I'm going to draw on that experience in creating this guide in ways that I hope are both respectful to mystics and creative departures from what we have in this world.