It is proper to recite Birkat Ha’mazon over a cup of wine. The one who leads the Birkat Ha’mazon holds the cup and then, after Birkat Ha’mazon, he recites the Beracha of "Boreh Peri Ha’gefen" and drinks the wine. Preferably, he should drink at least a Rebi’it of wine, so he can recite the Beracha Aharona.
Furthermore, it is proper to pass the cup around the table so that each person can sip from the wine upon which Birkat Ha’mazon was recited. As a rule, the people around the table do not recite a Beracha over the wine before sipping from the cup. Assuming that the one who recited the Beracha had in mind for the Beracha to apply to everyone at the table, and they, too, had in mind to fulfill their obligation through his recitation, they need not recite a Beracha before drinking the wine.
The exception to this rule, as the Shulhan Aruch writes (Orah Haim 190:5; listen to audio recording for precise citation), is a case of a large meal, where some participants might not expect to receive any wine. If many people take part in the meal, the cup will likely not contain enough wine for everyone at the table. Even if it does, some people at the other end of the table will naturally presume that the cup will be empty by the time it reaches them. As such, if in the end they in fact receive some wine, they must recite a Beracha. Since they did not anticipate receiving wine, they presumably did not have in mind while listening to the Beracha that it should fulfill their obligation, and they must therefore recite their own Beracha.
It thus emerges that those in close vicinity to the one who recited the Beracha do not recite their own Beracha, while those seated far away, who did not anticipate receiving wine, must recite a Beracha if there turns out to be enough wine for them.
Hacham David Yosef, in his work Halacha Berura (p. 535), adds that this would not apply if somebody explicitly had in mind for the Beracha to fulfill his obligation if the wine reaches him. Even if he is seated in an area where he cannot expect to receive wine, if while listening to the Beracha he had specific intent to fulfill his obligation, then he does not recite a new Beracha if he in fact does receive wine.
Summary: Birkat Ha’mazon should optimally be recited over a cup of wine. After Birkat Ha’mazon, the one who led the recitation should recite the Beracha over the wine, drink a Rebi’it, and then pass the cup around the table so that everyone can drink. The people do not recite a Beracha before drinking, as they fulfilled their obligation by listening to the Beracha recited by the one who led Birkat Ha’mazon. However, those people who were unsure whether they would receive wine must recite a Beracha, unless they had explicit intent to fulfill their obligation when they heard the initial Beracha, knowing that they might not get any wine.
