Since the Sages ordained that havdala be recited over wine, the cup should be held during havdala. It is held in the right hand, as it is the more important one. This preference for the right hand is true for all berakhot: Whenever a berakha is made over something, the object should be held in the right hand. Accordingly, when making the berakha over fragrance, the person making havdala should hold the fragrance in his right hand. During that time, many rest the cup of wine on a plate. Later, when they reach the berakha of Ha-mavdil, they pick up the cup once again. Some beautify the mitzva by holding the cup even while making the berakhot on the fragrance and the candle. Since the right hand has to be free to pick up the fragrance and to look at the candle’s flame, they pick up the cup in their left hand. When they reach Ha-mavdil they return the cup to their right hand (SA 296:6; MB ad loc.).
Some have the custom to sit for havdala, since by sitting the listeners establish that they wish to fulfill their obligation with this recitation of havdala (SA 296:6). Others customarily stand, demonstrating respect for Shabbat as it departs (Rema). In that case, in order to make it clear that everyone intends to fulfill their obligation by listening to havdala, they must gather round the person making havdala. Be-di’avad, if one stood at a distance but listened intently to the havdala, he has fulfilled his obligation.
As is the case with any kos shel berakha (a cup of wine linked to the performance of a mitzva), one should ensure that the cup is clean both inside and out. Many make a point of using a fancy goblet for havdala. The cup must hold a revi’it (roughly 75 ml and 150 ml according to Ĥazon Ish; see 6:5 above). If the cup has a larger capacity, it is a mitzva to fill it with wine, since it is appropriate to honor the berakha with a full cup. Although in most cases of kos shel berakha (e.g., for kiddush or at a wedding) it is preferable not to fill the cup all the way to the point of spilling over, many have the custom to fill the havdala cup to the point that it overflows a bit, as this is a symbol of blessing (Rema 296:1, and see 6:6 above for the rest of the laws concerning a kos shel berakha).
Ideally, the person making havdala should drink the entire revi’it of wine in the cup so that he can recite a berakha aĥarona over the wine. Nevertheless, to fulfill the mitzva of havdala it is sufficient to drink a melo lugmav (see above, 6:5, and n. 6 ad loc. regarding a case where one did not drink a cheek full; also see Peninei Halakha: Berakhot 10:10).
The audience must remain silent until the person making havdala finishes drinking a melo lugmav; since it is a mitzva to make havdala over a cup of wine, havdala is completed only when the person making havdala drinks a melo lugmav. Be-di’avad, if a listener speaks before the person making havdala drank from the cup, he has still fulfilled his obligation (SSK 60:39 and 48:6; see above, ch. 6 n. 10).