Kaede is a side character that can be unlocked by successfully convincing her to stay for sleep over just at the end of the party - to do so you need to have high "impression" value, have "drunkness" at 1 or 2 and have decent basic stats to have a better chance at convince her.
Once you unlock her, she will appear in Yuna's room on the same night after the party and every time it rains at night (there's base 30% chance for the rain to happen)
You can also use "rain stick" in the morning on any day, to make the chance of raining at night 100%, which will make kaede appear