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Davening Maariv after nightfall:
On the night of Shavuos, one is not to Daven Maariv prior to nightfall [Tzeis Hakochavim], even if this is normally done on Erev Shabbos or other Holidays. [This applies for both men and women.]
In light of the above, when are women to light the Yom Tov candles?
Some Poskim rule that women are to light the Yom Tov candles after nightfall, just as Maariv and Kiddush are to be said after nightfall. However, practically, the widespread custom is to light candles at the regular time of candle lighting.
If a woman did not light until nightfall, should she Daven Maariv before lighting if it is her custom to normally do so?
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.
Second day of Shavuos falls on Friday evening: See E!
Mentioning the giving of the Torah on Shavuos:
In the Shemoneh Esrei prayers of Shavuos one recites “Zeman Matan Toraseinu”, as explained in chapter 1. [In the event that one is keeping Shavuos on a different date due to traveling past the dateline, see chapter 1 in Q&A!]
When Shavuos 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.
If one forgot to say Vetodieinu in Shemoneh Esrei what is he to do?
Some Poskim rule once he has begun saying “Vatiten Lanu Hashem” he is not to go back to say Vetodieinu and is rather to continue with Shemoneh Esrei as usual. In such a case he must beware to say Baruch Hamavdil prior to doing any Melacha which is permitted on Yom Tov. Other Poskim however rule that one who does go back to say it has upon whom to rely, so long as he has not yet finished the blessing of Mikadeish Yisrael Vehazmanim.
Second day of Shavuos falls on Friday evening:
When [the second night of] Shavuos in the Diaspora 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 is recited instead of Berina. After Shemoneh Esrei one recites Vayechulu, and Meiyn Sheva. Following the recital of Meiyn Sheva one recites Kaddish with Tiskabel. This Kaddish is then followed by “Mizmor Ledavid Hashem Roiy” as is usually recited on Friday night. One then recites half Kaddish, Barchu and Aleinu.]
 Admur 494:2; Taz 494; Chok Yaakov 494:1; M”B 494:1; Lehoros Nasan 7:31; See Kaf Hachaim 494:1, Piskeiy Teshuvos 494:1
Other opinions: Some Poskim rule it is permitted to Daven Maariv prior to nightfall on Shavuos, and only Kiddush is to be avoided until nightfall. [Implication of M”A 494:1; Shelah Miseches Shavuos p. 179; Siddur Yaavetz; Daas Torah 494 in name of Masas Binyamin and Nachlas Shiva; Kaf Hachaim 494:1] Furthermore, some Poskim rule one may even say Kiddush prior to Tzeis Hakochavim, with intent to fulfill the Mitzvah of adding to Yom Tov. [Hisorerus Teshuvah 2:56] Practically, the widespread custom is to be stringent and delay Maariv and Kiddush until after nightfall. [Hisorerus Teshuvah ibid; Likkutei Maharich]
 The reason: Although on all eves of Holidays [and of Shabbos] one is allowed [and so was the widespread custom] to accept the Holiday earlier then its set time of sunset, and thus pray Maariv prior to sunset, nevertheless, on the Eve of Shavuos this may not be done. The reason for this is because if one were to accept the Kedusha of Yom Tov, through Davening Maariv, before nightfall, this would cause the 49 days of the Sefira to be slightly shortened, and hence one would lack a full 49 days prior to Shavuos, the 50th day. This is problematic being that the Torah requires there be 49 full days prior to Shavuos, as the verse states “Sheva Shabbosos Temimos Tehiyena”. [Admur ibid]
 Lehoros Nasan 7:31; See Kaf Hachaim 494:1, Piskeiy Teshuvos 494:2
The reason: As although women are not obligated in counting the Omer, nevertheless, the holiday of Shavuos is dependent on the passing of a full 49 days, and thus is not fulfilled when one accepts Yom Tov early. [ibid]
 Luach of Rav Tuchinsky; Piskeiy Teshuvos 494:2
 This especially applies due to the fact that the blessing of Shehechiyanu is recited by women during candle lighting, and this blessing seems to accept Itzumo Shel Yom of Yom Tov. [ibid]
 Hiskashrus 931
 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 494:1; Rivash 96; Peri Chadash 494:1; Chok Yaakov 494:1; See Likkutei Sichos 3:997
 Admur 491:4; 599:1; Michaber 599:1
 Mateh Efraim 599:7; See also Kaf Hachaim 599:3
 His reasoning is because doing so would require the person to repeat Hashem’s name in the blessing of Vatiten Lanu.
 Sheivet Halevy 9:23
 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 begin 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] To note that the Mitzvah of Simcha does not apply on Rosh Hashanah, and hence we recite Berina in Lecha Dodi as a normal Shabbos, thus the only reason that explains why on Rosh Hashanah we omit these Psalms is the last reason mentioned. [Glosses of Rav Raskin on Siddur p. 250]
 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 Maharich 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]
 Mateh Efraim 582:2; Otzer Minhagei Chabad p. 63
 The above order is written in Piskeiy Hasiddur footnote 40; Otzer Minhagei Chabad p. 69