Talk to her, give her gifts, have her do fortunes for you, choose her during festivals like the Sakura festival or the dance festival...etc.
She likes diamonds, I know that much o-O; And you can find those in the the winter-mountains place =/
Yup, complete all of her quests, the last one is either at 9 or 10 LP and she'll give you her marriage item (Crystal Ball). Then give it to her and you'll get married