Chacham Ovadia Yosef writes in his work Chazon Ovadia (p. 92; listen to audio for precise citation) that the Mitzva to recite Kiddush on Yom Tov is at night, according to most authorities, a Torah obligation. One must therefore be meticulous in his observance of this Mitzva, just as one must with regard to Kiddush on Shabbat.
The laws of Kiddush on Yom Tov generally correspond to those that apply to Kiddush on Shabbat. Thus, for example, one may not eat or drink anything on the evening of Yom Tov until he recites (or hears) Kiddush, just as on Shabbat. The Kiddush obligation on Yom Tov, like on Shabbat, includes both men and women. Similarly, Kiddush must be recited on Yom Tov "Be'makom Se'uda," in the place where one then partakes of a meal, just as on Shabbat. If a person could not, for whatever reason, recite Kiddush on the night of Yom Tov, such as if he was sick, he should recite the evening Kiddush during the day of Yom Tov, as the Shulchan Aruch rules with regard to Kiddush on Shabbat (271:8).
Halacha requires one to eat two meals on Yom Tov with Lechem Mishneh (two loaves of bread, or two whole Matzot on Pesach), one on the evening of Yom Tov, and the other during the day. One who did not, for whatever reason, eat a meal on the night of Yom Tov should eat two meals during the day of Yom Tov. The Chid"a (Rabbi Chayim Yosef David Azulai, 1724-1806), in his work Birkei Yosef (529:3), writes that the common practice among all Jewish communities is not to require Se'uda Shelishit (the third meal) on Yom Tov, even though this meal is obligatory on Shabbat. He writes that according to neither Halacha nor Kabbalah must one eat a third meal on Yom Tov. Only when Yom Tov falls on Shabbat is one obligated to eat Se'uda Shelishit.
Summary: The laws of Kiddush on Yom Tov correspond to those of Kiddush on Shabbat: one may not eat or drink before reciting or hearing Kiddush; the obligation applies to both men and women; Kiddush must be recited in the place where one then eats a meal; one who did not recite Kiddush at night recites the nighttime Kiddush during the day. On Yom Tov one must eat two meals with "Lechem Mishneh"; Se'uda Shelishit is not required on Yom Tov.
