Customs related to Havdala:
Wearing Shabbos cloths: It is proper to wear at least some of one’s Shabbos clothing until after Havdala on Motzei Shabbos. [See Halacha 27 for a full analysis on this subject]
Looking at the cup of wine and candle: While the blessing of Havdala is being recited the listeners are to look at the cup of wine and the candle. [Likewise the person saying Havdala is to look at the cup during the blessing.]
How much of the wine is one to drink? At the conclusion of the last blessing it is customary that one drink the entire cup of wine himself. It is not distributed to others to drink as is commonly done by Kiddush. [If however one said Havdala over the same cup of wine used for Birchas Hamazon, it may be distributed to others, including women.]
At the very least one must drink a Revius of wine in order to avoid doubt as to whether he is obligated in an after blessing. If one drank less than a Revius, then if he drank the majority of a Revius he nevertheless fulfills his obligation, and is not to say an after blessing afterwards. If he drank less than Malei Lugmav, or did not drink wine at all, it is disputed whether he has fulfilled his obligation, and practically he is not to repeat Havdala as Safek Brachos Lehakeil. [Rather he should try to hear Havdala from another person.]
Extinguishing the candle with the Havdala wine: After drinking the wine of Havdala the leftover wine which remains in the cup is customarily poured on the table [or plate, such as the Kiddush plate]. One then uses this wine to extinguish the Havdala candle by dipping the candle into it. [Practically however many have the custom to pour the wine over the candle, and not to first pour the wine onto a plate and then dip the candle into it. Others do both and dip the candle into the wine that is on the plate and then pour wine over it.]
Washing one’s eyes with the spilled wine:  It is customary to wet one’s eyes using the wine which was spilled to extinguish the candle. [The custom is to dip ones fingers into the leftover wine and to then pass them over the external part of the eye. This is a Segula for eyesight. Many have the custom to also pass the wine over the forehead and pockets of their clothing.]
Smelling the candle:
Some have the custom to smell the Havdala candle after it is extinguished in order to show belovedness to the Mitzvah. It is likewise recorded that doing so protects one from evil spirits. It however is not our custom to follow this practice.
The Shabbos tablecloth:
Some write one is not to remove the Shabbos tablecloth until after Havdala.
Blowing out a candle:
One is not to blow out a candle with his mouth. Thus in the event that one is unable to extinguish his candle with the wine he is to extinguish it in another way.
 296/15 as rules Rama 296/6 based on the Igur and Agguda; See Admur 213/5; 298/20
Other Opinions: The Michaber [ibid] rules Havdala is to be said sitting. Likewise all the listeners are to sit. This ruling is based on Tosafus and Moredchaiy which rule one is to sit in order so the blessing over the wine have a Kevius. [Kaf Hachaim 296/39-41; M”B 296/27] So rules also Gra [on Shulchan here and also in Maaseh Rav 150] Aruch Hashulchan 296/17 writes there are Gedolei Yisrael which recite it sitting. The Kaf Hachaim [Rav Falagi] 31/38 rules that based on kabala one is to sit while saying Havdala.
The reason why other Poskim do not require one to sit despite the above need of Kevius to be Yotzei others is because it was only said that one must sit to be Yotzei others in a case of Birchas Hanehin, such as when the listeners will be drinking the wine. It is not required simply to be Yotzei others for a Mitzvah. Thus here since no one else will be drinking the wine other than the person saying Havdala, it is therefore not necessary for them to sit. [Admur 213/5 regarding Haeish and Besamim; Alef Lamagen 625/74] Regarding the blessing of Haeish Admur further added there that no Kevius of sitting is required as Kevius is not needed by those pleasures that all the listeners receive equally. Hence by the blessing of Haeish everyone may stand.
Ruling of Sefaradim: Some Sefaradi Poskim rule like the Rama in this matter that Havdala is to be said standing. [Ben Ish Chaiy Vayeitzei 21] Others rule like Michaber that one is to sit. [Kaf Hachaim ibid; Yechaveh Daas 4/26]
 This is done in honor of the king which we are escorting when we say Havdala, and it is customary to stand when escorting the king. [ibid]
 The reason for looking at the wine and candle is because by a Kos Shel Bracha those listening are to look at the cup as writes Admur in 183/8
The person saying Havdala is to look at the cup of wine and candles. [Kaf Hachaim 296/8; Kitzur Halachos 296 footnote 12] However this applies only when he says the blessing over the candles. During the blessings of Hagafen and Hamavdil he is to look at the cup. [Kitzur Halachos ibid] and so is the custom of the Rebbe.
 As it is not proper for Torah Scholars to eat or drink while standing. [ibid] This applies also for those that are not Torah Scholars, and applies by all foods and drink, not just by Havdala. [Elya Raba 296/14; Beir Heiytiv 170/16; Kitzur Halachos 296 footnote 14]
 Seemingly this applies even if the cup contains more than a Revius, as if it contains exactly a Revius it would be an obligation to drink the entire cup in order not to enter into doubts regarding a Bracha Achrona. Hence from the wording of Admur that doing so is a mere custom it seems he refers even to when the cup holds more than a Revius.
 Admur ibid based on Shivlei Haleket brought in M”A 296/4
The reason for not distributing the wine to others: The Seder Hayom writes that he has not heard a reason as for why one drinks the entire cup himself although perhaps it contains some Kabalistic meaning. The M”B 296/6 writes that we do not want one to drink less than a Revius and then enter into a questionable after blessing. Kaf Hachaim of Rav Falagi writes we do not give to other men to drink being that it is customary not to give the women and we do not want to offend the women by singling them out. In Lekutei Torah of Rav M. of Chernobyl he writes that one must be very careful not to drink from the Havdala wine of another person as this causes enmity between them. The Divreiy Yichezkal p. 231 writes similarly that it causes rift in the family. [See Piskeiy Teshuvos 296/8]
The reason why women do not drinking wine of Havdala: In addition to the above reasons for why only the person saying Havdala drinks from the wine there are additional reasons for why women specifically should not drink from the wine. See Halacha 15 Q&A there!
Other Opinions: Some Poskim argue on the above and rule other men are to drink from the Havdala wine, as is the rule by any Kos Shel Bracha. [Elya Raba, brought in Kaf Hachaim 296/15; See Tur 299; Machzor Vitry 116; Leket Yosher p. 57]
 Ketzos Hashulchan 97 footnote 3 and 96 footnote 9 as the wine is considered a Kos Shel Bracha.
 So writes Admur in 472/19 “must”. However in 190/6 and in Seder he writes “Good” that it is merely proper to do so.
 190/6 Regarding Kos Shel Bracha as there is doubt in whether one must say an after blessing after drinking a Kezayis of wine, or only after a Revius of wine. [Vetzaruch Iyun on this omission from Ketzos Hashulchan 97/3]. So rules Admur also in 472/19 regarding the 4th cup of the Seder and in Seder Birchas Hanehnin 8/1]
 The amount of wine to fill one cheek. This is normally the majority of a Revius.
 190/4; Birchas Habayis 47/11; Kaf Hachaim 296/16; Piskeiy Teshuvos 296/11
The first opinion there [190/4] rules it is an obligation for a Jew to drink the wine of Kos Shel Bracha. The second opinion there rules it is not an obligation to drink the wine, even though one said a blessing over it. Practically Admur concludes Safek Brachos Lehakeil.
Requires further analysis: Tzaruch Iyun Gadol from the ruling of Admur in 295/4 [brought later in Halacha 18] that if one did not have an adult which is fulfilling his obligation drink the Havdala wine, no one has fulfilled their obligation with this Havdala. [Ketzos Hashulchan 97 footnote 6; Tehila Ledavid 295/5; See Kitzur Halachos Miluim p. 109-112, and later on in Halacha 17]
Other Opinions: According to the M”B 296/9 if one did not drink Malei Lugmav of the wine he has not fulfilled his obligation.
 Piskeiy Teshuvos ibid
 The reason this is done is in order to show to all that the candle was lit simply for the Mitzvah of saying a blessing over it and not in order to use its light. (Therefore if one is saying Havdala over a candle which was not lit for this purpose, but for its light, it does not need to be extinguished.) [ibid]
 Seemingly the reason for the change of custom is because today we are accustomed to have some of the wine overflow onto the plate before even beginning Havdala, hence there is no need to pour wine onto the plate after Havdala to use to extinguish the candle. Thus they rather pour onto the candle.
 See Piskeiy Teshuvos 296 footnote 63
 This is done out of belovedness for the Mitzvah. [ibid]
Other reasons: Using the leftovers of a Mitzvah refrain evil from befalling a person. [Pirkeiy Derebbe Eliezer 20; Gra on Rama 296/1]
 Shaareiy Halacha Uminhag 157; See Perisha 269/3
Other Customs: Some have the custom to dip their fingers and place them over the eyes three times. [Mishmeres Shalom Minhagim] Some have the custom to recite the verse “Mitzvas Hashem Bara Meiras Eiyanyim”. [Kitzur Shlah in name of Arizal; Siddur Yaavetz] There exists different customs regarding which finger to dip into the wine. Some dip the pinky, others the index finger which is near the thumb. [Piskeiy Teshuvos 296 footnote 65]
 Piskeiy Teshuvos 296/7
 Siddur Yaavetz; Ketzos Hashulchan 97 footnote 7; Ashel Avraham Butchach 297; Minchas Shabbos in Shiyureiy Mincha 96/5
The Ketzos Hashulchan ibid testifies of the custom of the Sdei Chemed in Chevron to smell the Havdala candle after it was extinguished and he would exclaim “Ah Ah” very loudly. Everyone in the presence would break in laughter.
 Minchas Shabbos ibid in name of Sefer Zechariya
 Shaareiy Halacha Uminhag 5/35
 M”B 262/4 in name of Elya Raba and Aguda
 Piskeiy Teshuvos 296 footnote 71 in name of Kaf Hachaim [Falagi] 31
 This is said to be of danger to the person. [ibid]