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The order until Shemoneh Esrei:
For Maariv of Yom Tov, some are accustomed to read the added Mizmorim that are said on Shabbos. The Chabad custom on the night of Yom Tov is to recite a regular weekday Maariv prayer until Shemoneh Esrei, without any of the additional Mizmorim that are normally added on Shabbos.
Saying Hallel on the first nights of Pesach:
The widespread custom of many communities is to recite the complete Hallel with a blessing on both nights of Yom Tov [in the Diaspora]. Practically, so is the Chabad custom. In Eretz Yisrael, Hallel is only recited on the first night. After Hallel, one is to recite Kaddish with Tiskabel.
If one is Davening without a Minyan, is he to say Hallel with a blessing?
If one’s custom is not to say Hallel what is he to do if he is Davening in a Shul that Hallel is said?
He is to say Hallel together with the congregation, although without a blessing.
Pesach falls on Friday evening:
When [the first night of] Pesach falls on Friday evening, one begins the Maariv prayer from Mizmor Ledavid [psalm 29], [omitting all the Psalms from Lechu Neranina until Mizmor Ledavid]. [One recites the entire dialect from Mizmor Ledavid and onwards, including Ana Bekoach; all the stanzas of Lecha Dodi; Mizmor Shir, Kegavna. In Lecha Dodi, the wording of Besimcha instead of Berina is recited. In Shemoneh Esrei one needs to mention “Shabbos” in the beginning of the middle blessing, and in the conclusion of the blessing. After Shemoneh Esrei one recites Vayechulu. One does not recite Meiyn Sheva and rather proceeds to recite Hallel. After Hallel one recite Kaddish Tiskabel, Mizmor Ledavid. One then recites half Kaddish, Barchu and Aleinu.]
Pesach falls on Motzei Shabbos:
When Pesach falls on Motzei Shabbos [i.e. Saturday night], then in the evening prayer of Shemoneh Esrei the paragraph of Vetodieinu/ותודיענו is added prior to the paragraph of ותתן לנו.
 Admur 488:1; It is unclear what additions Admur is referring to in the Maariv prayer. Perhaps it refers to the prayer of Mizmor Shir Leyom Hashabbos. [See P”M 488 A”A 1] However, the Poskim negate this recital during Maariv of Yom Tov. [Chok Yaakov 488:1; Machatzis Hashekel 488:1; P”M 488 A”A 1] Alternatively, it refers to Lechu Neranena, or Lecha Dodi. [P”M ibid] Practically, on a Yom Tov that falls on a weekday, a regular Maariv prayer is followed until Shemoneh Esrei without any additional Mizmorim that are normally added on Shabbos.
 Admur 487:8 that so is custom of some; Siddur Admur; Michaber 497:4; Gr”a
 So is the custom of Sefaradi, Chassidic and some Litvish Jewry. The Rama ibid however rules the custom in his provinces is not to say Hallel and so is brought as the second custom in Admur ibid. Practically, today, even amongst Ashkenazi communities, many are accustomed to recite Hallel as was the custom of the Gr”a.
 Igros Moshe 4:94
 Igros Moshe 4:94
 The reason: As otherwise this would be transgressing “Lo Sisgodedu”. [Igros Moshe ibid]
 Siddur Admur regarding Yom Tov; Ketzos Hashulchan 77:2; Shaar Hakolel 17:6 states that this was mistakenly omitted from certain prints of the Siddur
Other customs: Some are accustomed to beginning Maariv from after Lecha Dodi, by Mizmor Shir. [M”E 625:41]
 The reason: Some write the reason is because there is a Mitzvah of Simcha on Yom Tov and we hence desire to speed the conclusion of Maariv. [Otzer Minhagei Yeshurun p. 64; See Admur 270:1 regarding Bameh Madlikin that it is omitted on Yom Tov in order to hasten Simchas Yom Tov] Alternatively the reason is because these Psalms contain the words Rina, and on Yom Tov we emphasize the words Simcha. [Ketzos Hashulchan 77 footnote 13] Alternatively, the reason is because the first five Mizmorim until Mizmor Ledavid relate to the five weekdays until Erev Shabbos while the psalm of Mizmor Ledavid relates to Erev Shabbos. Hence, we omit the first five Zemiros as it is not proper to relate them to Yom Tov. [Sichas Kodesh 2 p. 121]
 Shaar Hakolel 17:6; Ketzos Hashulchan 77 footnote 13; Otzer Minhagei Chabad p. 63
Other customs: Some are accustomed to only recite the first and last stanza of Lecha Dodi. [M”E 625:41] Others recite the first two stanzas of Lecha Dodi corresponding to Zachar and Shamor. [Alef Hamagen 625:56] Others recite the entire Lecha Dodi with exception to the stanza of Hisnaari Meiafar Kumi which is omitted. [Peri Megadim] Some are accustomed to omit Kegavna being that it mentions that all the other days are filled with wrath which is untrue regarding Yom Tov. [Siddur Yaavetz; Likkutei Mahrich Pesach; Alef Lamateh 625:67; Divrei Torah 9:72; Piskeiy Teshuvos 487:3]
 Hagahos Hasiddur of Rebbe Rashab; Ketzos Hashulchan 77:2; Mishnes Chassidim “Leil Yom Tov” 1:2].
Difference between Rina and Simcha: The term Rina denotes a bittersweet joy, a joy that comes as a result of a previous distance. However Simcha does not have any bitterness mixed with it at all. [Magen Avos Vayishlach’ Ketzos Hashulchan 77 footnote 13]
 If one forgot to mention Shabbos in any area he must repeat the prayer. If it was mentioned anywhere in the prayer, it is valid, whether it was mentioned in the middle blessing or in the concluding blessing. [Admur 487:3]
 The above order is written in Piskeiy Hasiddur footnote 40; Otzer Minhagei Chabad p. 69
 Admur 487:4
 The reason: The reason for this is because it the night of Pesach is considered a Leil Shimurim. [Admur ibid]
 Admur 491:4; 599/1; Michaber 599/1