The Amida on Yom Tov (the following describes all prayers, except for Musaf, of all holidays except Rosh Ha-shana) has seven berakhot, just like the Amida for Shabbat. The formulations of the first three and last three berakhot are the same as those of the weekday Amida. In the middle, instead of the 13 petitionary berakhot recited during the week, the Yom Tov Amida has one berakha, whose theme is the sanctity of the holiday. It mentions the name of the specific festival and invokes God’s election of Israel from among the nations, sanctifying us with His mitzvot, bringing us close to His service, and giving us the festivals on which to rejoice and to recall the Exodus from Egypt. With this awareness, we ask that memories of us should ascend and come before (ya’aleh ve-yavo) God and be viewed positively. We conclude with the paragraph of Ve-hasi’enu, asking that God elevate us through the sanctity of the festivals, sanctify us through His mitzvot, give us a share in His Torah, purify our hearts to serve Him truly, and grant us the privilege of celebrating the festivals joyously. We conclude, “Blessed are You, Lord, Who sanctifies Israel and the seasons.”
Technically, the Shabbat and Yom Tov Amida could have included all the petitionary berakhot in addition to a special berakha in honor of Shabbat or Yom Tov. However, out of respect for Shabbat and the holidays, the Sages did not want to impose upon people all the berakhot recited during the week (Berakhot 21a). Furthermore, on Shabbat and Yom Tov it is not appropriate to make requests for immediate needs, thoughts about which are likely to lead to worry (Tanḥuma; Rashi; Rambam). Therefore, the Sages instituted one middle berakha instead of the usual 13. Nevertheless, if one realizes that he is mistakenly reciting the berakhot of the weekday Amida, he should conclude that berakha and then proceed with the appropriate berakha for Yom Tov or Shabbat. Since, technically, the weekday blessings could be recited, and since he has already begun a berakha, it is proper for him to finish it (SA 268:2; MB ad loc. 3; for Musaf see section 9 below).
If one omits the name of the festival in the Amida, or mentions a different festival or Shabbat instead, he has not fulfilled his obligation, and must return to the beginning of the berakha and recite it correctly. If he has already finished the Amida, even if he has not stepped backwards, he must repeat the Amida (MB 487:11). However, if one is reading the Amida from a siddur and is aware of the name of the festival but does not remember mentioning it, he may assume that he did so (Kaf Ha-ḥayim 487:30).
It is customary to use special melodies for the Shabbat and Yom Tov prayers, with Shabbat and Yom Tov each having its own melodies (Mateh Ephraim 625:40).
There is a custom from the time of the Rishonim to add psalms to the Pesukei De-zimra section that introduces Shaḥarit. At the conclusion of Pesukei De-zimra, we add the prayer of Nishmat.