Instructions
Play through the storyline until the date in game is May 17. This is when the story event to unlock Yukiko's Social Link stat occurs. Nothing you do can improve or hinder your ability to date Yukiko before this event occurs.
Equip the Priestess Persona. Possessing the Priestess Persona improves the effectiveness of any interactions you have with Yukiko.
Invite Yukiko whenever you have to choose a friend's name from a list. This includes when you can invite someone to lunch, invite someone to an event, pray for someone at the shrine, dream about someone or perform any other interaction. Any situation where you select a friend from a list improves the Social Link stat with the friend that is selected.
Agree to go with Yukiko whenever she calls you at home.
Repeat Steps 3 and 4 until Yukiko says that she loves you. At this point, you start dating her unless you choose the speech option to refuse her love.