One person, designated as the Symposiarch, was responsible for keeping the revelry under control. He managed the servants and the dilution of the wine. Greeks never drank wine full strength because they thought only drunkards and people of low quality would do so. The typical dilution was 1:3 wine to water.
The Kylix was a drinking vessel used to drink water or wine. When the Greeks copied drinking vessels from the orient, they added handles and a base. The handles were held when drinking, the base when toasting. The Kylix had an image painted in the bottom (often erotic) so as the drinker empted the vessel, the image would be revealed. It was also used in a game called kottabos where the wine residue was tossed from it to a target.