If one did not say Havdala on Motzei Shabbos:
The main Mitzvah of Havdala is to say it at night on Motzei Shabbos. If one did not do so, whether due to forgetfulness or advertently, he is to say Havdala on Sunday. In such a case it is forbidden for him to eat or drink anything, with exception to water, until he says Havdala. If he began eating or drinking and then remembered, he must immediately stop eating or drinking and say Havdala.
If one did not say Havdala on Sunday, he is to do so on Monday prior to eating. If one did not say Havdala on Monday, he is to do so on Tuesday prior to eating. If he did not say Havdala on Tuesday [prior to sunset] he can no longer say it.
Is the blessing of Besamim and Haeish recited? In the event that one is saying Havdala on Sunday or onwards, he does not recite the blessings of Besamim or Meoreiy Haeish. Thus immediately after the blessing of Hagafen he is to begin the blessing of Hamavdil.
If one remembered to say Havdala on Sunday-Tuesday and that day is Yom Tov: [If Yom Tov fell on Sunday, or Sunday and Monday, and one remembered on Yom Tov that he did not say Havdala in Kiddush-see Q&A! If Yom Tov fell on Monday and one remembered on Yom Tov that he did not say Havdala on Motzei Shabbos then some Poskim (see footnote) write he is to delay Havdala until Motzei Yom Tov, if Yom Tov will be over Monday night.] If Yom Tov fell on Monday and it is a two day Yom Tov, and hence Yom Tov will conclude on Tuesday night, or if Yom Tov fell on Tuesday and only then did he remember that he did not say Havdala, then if he remembered before Kiddush of the Yom Tov night meal, he is to hear Kiddush from another person, and then immediately say Havdala over a cup of wine, and then immediately wash for the meal. [If he remembered that he did not say Havdala after he already said Kiddush on Yom Tov night he is to stop and say Havdala as soon as he remembers. If he remembers before Kiddush of Yom Tov day he is to say Havdala over wine and then eat the meal.] In all the above cases that one is saying Havdala on Yom Tov the Nusach is “Bein Kodesh Lechol.
May one who did not say Havdala on Motzei Yom Tov say it the next day?
One who did not say Havdala on Motzei Yom Tov is to say Havdala the next day [until sunset], and is not to eat or drink anything, besides for water, until he does so. If one did not say Havdala the next day [prior to sunset] then he may no longer say Havdala, and may thus continue eating and drinking as usual.
What is one to do if he forgot to say Havdala in Kiddush of Yom Tov which falls on Motzei Shabbos?
He is to say Havdala over wine immediately upon remembering, whether he remembers that night or the next day. If he remembered before the Yom Tov day meal, he is to say Havdala over a cup of wine and then eat the meal. If one remembered only on Sunday night which is also Yom Tov, then he is to say Havdala within Kiddush.
If one remembered by Bein Hashmashos on Sunday: If Sunday night is Motzei Yom Tov then he is to wait until then, and when he recites Havdala for Motzei Yom Tov he fulfills Havdala also for Shabbos. If however that night is the second night of Yom Tov then he is to say Havdala by Kiddush of the Yom Tov night meal.
If one forgot to say Havdala on Motzei Rosh Hashana and then remembered on Tzom Gedalia what is he to do?
He should say Havdala on Tzom Gedalia and give the wine to drink to a child which has reached the age of Chinuch.
Is one who is saying Havdala on Sunday or onwards to still say the verses of Hinei Keil Yeshuasi?
Some Poskim bring it is not said in such a case, as it is only meant to be said on Motzei Shabbos. Vetzaruch Iyun
If one accidently recited the blessing of Besamim and Haeish while saying Havdala on Sunday –Tuesday is it considered an interval between the blessing of Hagafen and drinking the wine?
 Other Opinions: Chasam Sofer 17 rules if one advertently did not say Havdala on Motzei Shabbos he may not make it up on Sunday.
 This ruling of Admur follows the first opinion in Michaber 299/6
Other Opinions: Second opinion brought in Michaber [299/6] rules if one ate prior to saying Havdala over wine, then on Motzei Shabbos he may still say Havdala, however on Sunday or onwards he can no longer say Havdala. Admur rules one may say Havdala
 This applies even if he transgressed and advertently skipped Havdala on Motzei Shabbos-Sunday. [So is implied from Admur ibid and so rules M”B 299/15]
Background: This ruling of Admur follows the ruling of Rama 299/6 and the first opinion of Michaber ibid.
Other Opinions: The second opinion in Michaber rules one can only say Havdala up to Sunday and not any further. Kaf Hachaim 299/26 and Ben Ish Chaiy Vayeitzei 23 rule Safek Brachos Lehakel, and one may therefore not say Havdala past Sunday. Rather one may say it without Sheim Umalchus.
Difference between Sunday and other days: Some learn that the allowance to make up Havdala on Sunday is not from the laws of Tashlumin, but due to it still being part of the initial time of Havdala, as Motzei Shabbos is the night of Sunday. Their proof is from the fact Admur allows one to say Havdala on Sunday even if he advertently skipped Havdala on Motzei Shabbos. In such a case if Sunday was a status of Tashlumin he would not be able to say Havdala as is always the laws of Tashlumin that the advertent transgressor cannot make it up. [Chasam Sofer 17; Sdei Chemed Asifas Dinim Mareches Hei 15] The Rebbe however [Lekutei Sichos 31 Yisro 2 footnote 42] writes according to Admur all the days have the same status, as Admur did not differentiate in the Halacha [that if one missed Havdala purposely he cannot make it up past Sunday]. Thus all the days until Tuesday night are considered the days of Havdala, and not just as Tashlumin. The reason for this is because the entire Mitzvah is to remember Shabbos upon the leave of Shabbos, and the leave of Shabbos reaches until Tuesday night.
 Makor Chaim of Chavos Yair 299, brought in Piskeiy Teshuvos 299/10
 As the first three days of the week are considered the days after Shabbos, and are included in Motzei Shabbos. The last three days are however considered the days before Shabbos and have no connection to the previous Shabbos. [ibid]
 As the Sages only required blessing on the Besamim close to the leave of Shabbos [in order to comfort the soul]. Thus he may not say the blessing now in Havdala, as since it is no longer connected to Havdala it is considered an interval between the blessing over wine and its being drunk. [ibid]
 As the blessing of fire is only said the time it was first created which was Motzei Shabbos. [ibid]
 Based on 299/12
 Piskeiy Teshuvos 299/10
The reason for this delay is because there is question as to what should be the Nusach of Havdala on Yom Tov; perhaps he should say “Bein Kodesh Lechol” or perhaps “Bein Kodesh Lekodesh”. [M”A 299/9; Biur Halacha 299/6 “Ulikabel Achar Kach”]
However from Admur 299/11 it seems clear that the Nusach is “Bein Kodesh Lechol” and hence in such a case one is to say Havdala on Yom Tov itself being that it is forbidden to eat before Havdala. If he remembered prior to Kiddush of Yom Tov night then it follows the same law as the next case, see there.
 It is forbidden for him to say Havdala on the same cup of wine of which he is using for Kiddush as one may not say two “Kedushos” on one cup, as the Kiddush of Yom Tov is one Kedusha and has no connection to Havdala of Motzei Shabbos which enters into a weekday. This is in contrast to when Motzei Shabbos falls on Yom Tov in which case one does say Havdala on the same cup of wine, as since one recites “Bein Kodesh Lekodesh” in the Havdala they have a connection to each other, and are considered like one Kedusha. However in this case one would have to say Bein Kodesh Lechol it has no connection to the Kiddush of Yom Tov and therefore one may not say both of them on the same cup. [299/11]
What is one to do if he has no one else to hear Kiddush from? He is to say Kiddush over wine and then say Havdala over another cup of wine. [Piskeiy Teshuvos 299/10]
 He must say Havdala prior to Hamotzi as he may not eat until he says Havdala. [ibid]
 He must say Havdala and then wash for bread immediately after hearing Kiddush from another person in order for Kiddush to be followed by a meal within its required time. [ibid]
 So rules Admur 299/11 based on M”A 299/9
Other Opinions: The M”B in Biur Halacha “Ulikabel” leaves this matter with a great Tzaruch Iyun.
 For list of opinions on this question see Sdei Chemed Asifas Dinim Mareches Heim 15; Kaf Hachaim 299/24
 So rules Kol Bo 59; Rav Akiva Eiger 299/6; Beis Efrayim; Mishneh Berura 299/15; Piskeiy Teshuvos 299/4; SSH”K and so infers Sdei Chemed [Asifas Dinim Mareches Heim 15] from Admur 299/8 which allows saying Havdala of Shabbos the next day even if one purposely skipped Havdala at night, thus proving that the next say is not a Din Tashlumin, but rather a continuation of the obligation.
Other Poskim: The Sdei Chemed himself [ibid], rules as does the Chida [Bircheiy Yosef 491/1; Machazikei Bracha 491/1], Chesed Leavraham 491/2; Ben Ish Chaiy Vayeitzei 23 and many other Poskim listed by him, that one may not make up Havdala even the next day, as Safek Brachos Lehakel.
 However past sunset he is to no longer say Havdala as it is now a question whether or not the next day has begun, and many Poskim even hold that Havdala on Motzei Yom Tov may not be made up even the next day. Thus after sunset one is to be stringent. [So also rules Piskeiy Teshuvos 299/10]
 299/8 regarding Havdala after Shabbos, and the same rule applies to Motzei Yom Tov
 So is understood from all the Poskim mentioned in the first footnote which only extend the allowance for the next day.
Other Opinions: The Beis Yehuda 2/28, and other Poskim [brought in Sdei Chemed ibid] rule that one may say Havdala the entire week. We do not rule like this opinion, as brought in Chachma Umusur [see Sdei Chemed] that all the Poskim argued on his ruling. Likewise the Chida [Bircheiy Yosef 491/1; Machazikei Bracha 491/1] argues against his ruling.
 As it is forbidden for him to eat until he says Havdala. [Based on M”B 299/16]
 Har Tzevi 1/166
 Sdei Chemed Asifas Dinim Hei 15
 Lekutei Mahrich Seder Havdala
 Ashel Avraham Butchacher 299
 Rav Akiva Eiger brought in Biur Halacha 298/5 “Ein”