When does the fast begin?
All fast days [other than Tishe Be’av and Yom Kippur] begin by Alos Hashachar/daybreak. There is general dispute amongst the Poskim as to the definition of Alos/daybreak according to Halacha. Some Poskim, and calenders, rule Alos Hashachar begins 72 minutes prior to sunrise. Other Poskim, and calendars, rule Alos Hashachar begins 90 minutes prior to sunrise. Other Poskim, and calendars, rule Alos Hashachar begins two fluctuating hours prior to sunrise, and so is understood by many to be the opinion of Admur. [Practically, those who follow the rulings of Admur, are to be stringent like all opinions, and so is the widespread Chabad custom. Thus, regarding a fast day, one is to be stringent to consider Alos Hashachar to begin approximately two fluctuating hours prior to sunrise. Accordingly, even if one was awake the entire night, or went to sleep on condition to wake up before Alos to eat/drink, he must stop eating and drinking two fluctuating hours before sunrise. Being that different calendars follow different opinions regarding the definition of Alos, it is imperative that by a fast day, one look at a calendar which shows the time of Alos in accordance to the ruling of Admur, which is 2 fluctuating hours before Alos. [The correct time according to Admur can be found in Luach Kolel Chabad, Hiskashrus, Chabad Dvar Malchus, Luach of Rav Sangwai and certain Chabad websites. The time of Alos for a fast day found on Chabad.org is not accurate according to the above understanding of Admur.]
The fast begins from Alos Hashachar, although since there are various opinions in Poskim, and calendars, regarding the time of Alos Hashachar, one is to speak to his Rav for a final ruling of which opinion and calendar to follow. The suggested approach for those who follow the opinion of Admur, is to be stringent to stop eating and drinking starting from 120 fluctuating minutes [when the sun is 26 degrees below the horizon], and follow a calendar that uses this time.
 See Michaber 550:2 “One is not required to start fasting Mibiod Yom”
 Rashal Pesachim 2a; Minchas Kohen 2:6; M”A 89:2; Levush 261 and 459; Admur in 89:1, 184:3, and 261:5; Derech Hachaim; M”B 89 in Biur Halacha “Veim”; 58 Biur Halacha “Kemo”; and chapters: 92; 163; 235; 261; 459; This opinion is based on the calculation that there are 18 minutes per Mil [as rules Terumos Hadeshen 123; Michaber 459:2; Yoreh Deah 69:6; Rama 261:1; Admur in 89:1, 184:3, and 261:5] and there are 4 Mil between Alos and Neitz [as rules Rebbe Yehuda in Pesachim 94a] Accordingly there are 72 minutes before Alos, as 18 x 4=72.
 Gr”a 459; Chok Yaakov 459:10; Chasam Sofer in glosses 89] This opinion is based on the calculation that there are 22.5 minutes per Mil [as rules Mahril in Hilchos Pesach] and there are 4 Mil between Alos and Neitz [as rules Rebbe Yehuda in Pesachim 94a] Accordingly there are 90 minutes before Alos, as 22.5 x 4=72.
 Ruling of Admur in accordance to Harav Hagaon Avraham Chaim Naah printed in Shiureiy Mikveh 37; Yagdil Torah Tzemach Tzedek 23 p. 23 [see there for a full organized summary on the subject]; See Shiureiy Tziyon 37; Yagdil Torah Tzemach Tzedek 23 p. 23; Siddur Raskin p. 625 and Miluim 27 [summary of opinions according to Admur]; Rav Sangwai in Habracha 5:162 [defends and proofs the opinion of Gra”ch Naah in Admur and that so learned the Rebbe to be the opinion of Admur]; Piskeiy Teshuvos 89:2
Rulings of Admur: Admur wrote different calculations regarding Alos Hashachar throughout the Shulchan Aruch, Siddur and Tanya. This created confusion as to Admur’s opinion as to the time of Alos Hashachar. From 89:1, 184:3, and 261:5 it is calculated that Alos Hashachar is 72 minutes before sunrise, or possibly 96 minutes. In 249:3, 459:10 and the Siddur [Seder Hachnasas Shabbos] it can be calculated that Alos Hashachar is 96 minutes or 120 minutes before sunrise. From the time of Alos mentioned in the Siddur regarding Sefiras Haomer it is possible to calculate it as 72 or 120 minutes. In Igeres Hateshuva 3 Admur extends the time of starting a fast to three hours before sunrise. The following are the opinions of Chabad Rabbanim in this matter:
Opinion of Admur according to the Gra”ch Naah-Two fluctuating hours: Rav Avraham Chaim Naah ruled that according to Admur, Alos Hashachar begins two fluctuating hours prior to sunrise. [Shiureiy Tziyon 37; Yagdil Torah Tzemach Tzedek 23 p. 23] The calculation is as follows: There are 5 Mil between Alos and Neitz [as rules Ula in Pesachim 93b]. Each Mil is 24 minutes [as rules Rambam in Pirush Hamishnayos Pesachim 3:2]. Thus 24 minutes per Mil x 5 Mil between Alos and Neitz equals 120 minutes. [This follows the ruling of Admur in 249:3; 459:10 and Siddur and so rules regarding 24 minutes per Mil: Peri Chadash Y.D. 69:26; Kitzur SHU”A 36:11. However, in 89:1 and 261:5 Admur rules that there is only 4 Mil between Alos and sunrise, hence there is only 96 minutes between Alos and sunrise. As well, although in 459:10 Admur rules that the day begins from sunrise and ends by sunset, in 89:1 he rules that it begins from Alos until nightfall. Nevertheless, the final ruling of Admur follows the ruling of the Siddur in which Admur rules like in 459:10.]
Other opinions amongst Chabad Rabbanim: See article of Rav Raskin in Siddur Miluim 27, and Rav Sangwai in Habracha, for a summary of opinions of Chabad Rabbanim regarding the time of Alos Hashachar according to Admur. The opinions vary between 120 minutes, 72 minutes, 90 minutes and 96 minutes.
Opinion of three hours before sunrise: In Tanya, Igeres Hateshuva 3, Admur writes that one may eat up to three hours before sunrise, of a penitential fast. This implies that by a fast day one is to begin fasting even before Alos, when 1:3rd of the night has entered. [See Igros Kodesh 18:557] It requires further analysis however if this applies to all fasts, or just a penitential fast. [Sefer Haminhagim p. 45] However, from Admur in Siddur by Sefiras Haomer, it is implied that one may eat on a fast day up until Alos. [Hiskashrus 424:18 footnote 113] Likewise, Rav Groner states that he heard clearly from the Rebbe that the three hours is only applicable by a penitential fast. [Hiskashrus] However in Sichos Kodesh 2:494 the Rebbe mentioned a scrupulousness to begin the fast some time before Alos Hashachar. Vetzaruch Iyun.
 Definition of fluctuating hours: This means that the hours fluctuate in the winter and summer. Some Poskim rule this means it fluctuates in terms of Zmaniyos, meaning that it depends on the amount of hours in the day. Thus in the summer, the hours will be longer [between 120-150 minutes for two hours] while in the winter they will be shorter [between 90-120 minutes for two hours]. [So rules Minchas Cohen 2:6; Rama 233; Peri Chadash 58] However the Alter Rebbe and Gr”a both rule that it follows not the amount of hours in the day but rather the degree of distance of the sun from the horizon. [Admur in Seder Hachnasas Shabbos; Gr”a in 261; See Shut Mahrshag 2:34 quoted in Piskeiy Teshuvos 89:2 footnote 59 that this is the way we rule.] Thus, those who hold that Alos is 72 minutes it ends up being in Tishrei and Nissan 16.1 degrees from the horizon and the amount of time it takes the sun to travel to the horizon fluctuates between winter and summer. [See Piskeiy Teshuvos 89:2] According to Admur however who holds of 120 minutes, this would be when the sun is 26 degrees below the horizon.
Other opinions: Some Poskim rule we always measure the hours as set hours and hence there will always be only 120:90:72 minutes between Alos and sunrise at all times. [Admur 89:1; Birkeiy Yosef 261:1; Peri Megadim 261 A”A 9; Derech Hachaim; Siddur Yaavetz; Machatzis Hashekel 235:3]
 Shiureiy Tziyon ibid; It is important to note that there are Chabad Rabbanim who take a different approach in their understanding of the opinion of Admur, and each person is to follow his Rav. [See opinions of other Chabad Rabbanim in previous footnotes.] Those, who do not necessarily follow the rulings of Admur, should speak to his Rav for a final ruling regarding this matter, and which time, and calendar he should follow.