Following Shabbat, we recite Havdala, which includes 3 brachot: On wine or grape juice (reciting Borei Pri HaGafen); on spices, such as cloves or cinnamon (reciting Borei Minai B'Samim); and on a multi-wicked candle (reciting Borei M'orei Ha-esh). Though whiskey or beer may be used, wine is the preferred beverage. Indeed, Rav Yochanan says (Pesachim 113) that three people inherit Olam Haba: One who lives in Israel, one who trains his children to study Torah, and one who says Havdala over wine (preferably if this wine is left over from Kiddush earlier in the day). One should fill the wine to the brim, overflowing, symbolizing that our blessings should be overflowing.
It is a custom in many places for only the person reciting Havdala to drink from the cup; this may be to insure that one has drunk enough wine - 3 oz. - so as to justify saying a Bracha Achrona, and this is why some actually extinguish the Havdala candle by placing it in the cup. In other places, the cup is shared with guests.
The man of the house, rather than the wife, usually says Havdala, in part because some maintain that this is a time-bound positive Mitzva upon which women are exempt. But if the woman is alone, then she should say the Havdala herself - at least according to Ashkenazic custom - though most authorities say she should recite the bracha on the fire only after concluding Havdala and drinking the wine. As for the mysterious belief that if women drink Havdala wine they will grow hair in unwanted places? That is a classic "Bubba Meise" (old wives' tale) that has no basis in Halacha. (With thanks to Rabbi Ari Zivotofsky)