Picard, Bev Crusher, O'Brien, Worf, and Wes Crusher are your opponents in this drinking game. All of them must be defeated or you lose in disgrace.
The game has two recovery items: the bread and the warp coolant. Despite the differences in the text, they both recover almost the same amount of drunkenness. The number one danger is that you will click "Drink" after your opponent is already defeated, inflicting unneeded intoxication upon yourself. It sometimes takes a second for your opponent to start spewing, so the best thing to do is start watching closely after several drinks. A good way to progress is to take on one strong and one weak drinker, use a recovery item, then take on two moderate drinkers, use the other recovery item, and finally take on the last drinker. (Picard and Worf are strong drinkers; Bev Crusher and O'Brien are moderate drinkers; Wes Crusher is the weak drinker.) Alternatively, you can take on one strong and one weak drinker, use an item, take on the other strong drinker, use another item, and take on the two moderate drinkers.
After the crew has been defeated, return to the menu for the victory screen.