A number of Halachic authorities, including the Rama (Rav Moshe Isserles of Cracow, 1525-1572) and the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), record a custom to pour some wine out of the Habdala cup after the conclusion of Habdala, and then extinguish the candle in the wine that was poured. It is also customary to take some of the leftover wine and place it on one’s eyes and face. This is done for the purpose of Hibub Misva – to demonstrate our love and affection for the Misvot. The Hid"a (Rav Haim Yosef David Azulai, 1724-1806) emphasizes that one should not underestimate the importance of "Shiyureh Misva" – the "leftovers" of a Misva. Showing our love for that which had been used for a Misva, even if it only the "leftovers," is very significant, and has the power to save a person from calamity.
The Rama also writes (as understood by the Aruch Ha’shulhan) that it is customary to fill the cup before Habdala all the way to the rim, so that some wine will automatically spill when one lifts the cup, as an overflowing cup can bring blessing. This is mentioned also by the Ben Ish Hai, and this is, indeed, the accepted practice.
Although it is customary to add several drops of water to one’s cup of wine on other occasions, Rav Haim Vital (1542-1620) taught that this is not done with the Habdala cup.
The Shulhan Aruch writes that one may not recite Habdala over bread. Kiddush may be recited over bread, because Halacha requires reciting Kiddush in the framework of a meal, and thus the Kiddush is connected to the bread. Habdala, however, does not need to be recited in the framework of a meal, and thus there is no connection at all between Habdala and bread. As such, one may not recite Habdala over bread.
One may, however, recite Habdala over "Hamar Medina." Hacham Bension Abba Shaul (Israel, 1923-1998) and Hacham Ovadia Yosef understand this term as referring to intoxicating beverages which are commonly drunk in the country where one lives. In contemporary society, this would include beer, scotch, cognac, brandy, and the like. (Arak would likely qualify as "Hamar Medina" in Israel; it is doubtful whether it would qualify here in the United States.) Ashkenazim, following the ruling of Rav Moshe Feinstein (Russia-New York, 1895-1986), maintain that even non-alcoholic beverages qualify as "Hamar Medina," and thus they allow reciting Habdala even over milk, tea, coffee and the like. The only criterion according to Ashkenazic tradition is that the beverage must be something that a host would serve to a guest for honor, and not merely because the guest is thirsty. Sephardic tradition, however, as noted by both Hacham Bension Abba Shaul and Hacham Ovadia Yosef, does not follow this view, and allows reciting Habdala only on alcoholic beverages.
The Mishna Berura (Rav Yisrael Meir Kagan, 1839-1933) maintains that "Hamar Medina" may be used for Habdala only if one does not have wine. One who has wine must, according to the Mishna Berura, use it for Habdala. Hacham Bension Abba Shaul, however, disagrees, noting a clear distinction between the Shulhan Aruch’s formulations in the contexts of Kiddush and Habdala. In discussing the laws of Kiddush, the Shulhan Aruch writes that one who does not have wine may use "Hamar Medina" for Habdala, whereas in the context of Habdala, he writes simply that one is allowed to recite Habdala over "Hamar Medina." The clear implication is that "Hamar Medina" is acceptable for Habdala even if one is able to recite Habdala over wine. Hacham Ovadia Yosef, in Hazon Ovadia, appears to disagree with Hacham Bension’s conclusion, as he writes that "one who does not have wine" may recite Habdala over "Hamar Medina." It would therefore appear that one should preferably use wine for Habdala, but one who does not enjoy drinking wine may certainly use beer or other intoxicating beverages, in accordance with Hacham Bension’s position.
Strictly speaking, it suffices to drink just 1.7 ounces or so of wine from the Habdala cup. However, since there is a debate among the Halachic authorities as to whether one who drinks this amount of the Habdala cup recites a Beracha Aharona, one should preferably drink a full Rebi’it – 3.2 ounces – so that he will be required to recite a Beracha Aharona according to all opinions.
Summary: One should preferably use wine for Habdala, but one who does not like wine may use another common alcoholic beverage, such as beer. Although Ashkenazim allow using non-alcoholic beverages for Habdala, Sephardic practice requires using an intoxicating beverage. One should drink at least 3.2 ounces of wine from the Habdala cup. It is customary to fill the cup to the top before Habdala, so that some wine will spill out when one lifts the cup. It is customary after Habdala to spill out some wine and use that wine to extinguish the candle, and to place some wine on one’s eyes and face.