It was specifically a female duty to get water for the household. In wealthier families, slave women would be sent, while in poor households, the wife and daughters would perform this task. Water could be obtained from public fountain houses in the Agora. A chorus of women in Aristophanes' Lysistrata complain about the unpleasantness of the experience (317-31):
For I ... filled my water jar from the fountain with difficulty early in the morning in the midst of a crowd, noise, and the clattering of earthenware, jostled by slave women, some wearing brand marks [indicating who owned them - this detail reveals the contempt that the free women have for their slave counterparts]...There was a fountain house in the southeastern part of the Agora that may have been the famous Enneakrounos ("having nine spouts") or Kallirrhoê (= 'beautifully flowing' ) built by Peisistratus, the sixth century Athenian tyrant or his sons. Fountain houses like this one provided to the public free access to water, which earlier had been controlled by aristocratic well owners. It was typical of these fountain houses to have animal heads as decorative spouts. In the vase painting above, water juts forth from a lion's head on the far left; in the image below there are two lion head spouts facing the viewer and a donkey head spout on the far right.
Below is the water jar (hydria), from which the depiction of the women carrying water jars above is derived. Appropriately the painting demonstrates the use of the jar itself.