Ancient Greeks drank water and wine. Beer wasn't popular.
Water was collected each morning from springs, wells, and, occasionally, public fountains, and carried back to the home. The most famous spring in Athens was called Kallirhoe. It was a tradition to wash in the waters of Kallirhoe on your wedding day.
Most cups were as normal-looking as modern ones, but some were works of art. The pictures left and right are of a cup in the Metropolitan Museum in New York. It's the sort of thing you would have found in a wealthy house.
And if you think people took their art seriously back then, check out this cup:
Don't ask me how they got it to stand upright.