The bowls were situated at the left corner of the Altar going up, and the wine was poured from there into the deep ducts. The priest would go down into the ducts once in seventy years, bring up the congealed wine, and burn it. Others say that the ducts were there from the beginning of creation, and no cleaning was needed. The hint to this is in the Song of Song, "Your concealed thighs are the work of a master craftsman." From here, Talmud learns that Torah study and good deeds are to be done in private.
The water used for libation cannot stay overnight and cannot be left uncovered. In general, uncovered water should not be used because snakes may drink from it. Here, even using a filter would not help because of the idea that if you would not present something to a ruler, you would, of course, not do it for God.
Art: The Art of Painting (detail) by Johannes Vermeer