What must a woman do who kissed a man who is not her husband with desire during the daytime in Ramadan, and then broke her fast, thinking that her action invalidated the fast?

You made a mistake by kissing a foreign woman in Ramadan, and by acting upon an incorrect fatwa that states kissing absolutely invalidates the fast. Scholars are in agreement that kissing does not invalidate the fast unless it leads to ejaculation. Your third mistake was permitting yourself to break the fast for the rest of the day after intentionally breaking it.

What is incumbent upon you is sincere repentance and making up for that day. Expiation (kaffarah) is not obligatory upon you according to the correct opinion, which is the view of the majority of scholars, because expiation is only obligatory for breaking the fast through sexual intercourse.