Search for nine stones with which you can play a game with her. These stones spawn randomly around large rock formations near the tent in which she sits. They appear as black river stones and are difficult to see, especially if you are sitting on a mount. See the talk page for tips (including video) on how to best find them.
Return to Ootani and give her the stones.
Play a tic-tac-toe-style game with her. After you win speak to her for update.