It is the task of the women to go for the household water to the well or spring. And they do it today in many places in the East just like it was done when the Genesis account speaks of it being "the time of the evening, even the time that women go out to draw water" (Genesis 24:11).
The women are trained to do this from girlhood, for Saul and his servant "found young maidens going out to draw water" (I Samuel 9:11). The chief time for doing this is in the late afternoon or evening, although it is often done early in the morning. Earthenware pitchers (Lamentations 4:2) are used for the purpose, and they have one and sometimes two handles. It has been customary for Syrian women to carry the pitcher of water on their shoulder, although sometimes it is carried on the hip. Most Arabs of Israel carry it upon their head. Scripture says that Rebekah carried her pitcher on her shoulder (Genesis 24:15).
Carrying a pitcher of water was all but universally done by women. It must have been a picturesque sight to see them going and coming with the pitcher poised gracefully upon the head or shoulder. When JESUS instructed two of his disciples, "Go ye into the city, and there shall meet you a man bearing a pitcher of water: follow him" (Mark 14:13), that would be an easy way of identifying the person, for it is exceedingly uncommon to see a man carrying a pitcher of water, which is a woman's task. When larger supplies of water are needed, men use large skins of sheep or goats for carrying the supply. The pitchers are reserved for the use of the women. There is nothing left at the well that may be used for drawing water from a depth. Each woman who comes for water brings with her, in addition to the pitcher in which to carry the water, a hard leather portable bucket with a rope, in order to let it down to the level of the water. The Samaritan woman whom JESUS met at Jacob's well had brought all this with her, but JESUS did not have such equipment with him. Hence she said to him: "Sir, thou hast nothing to draw with, and the well is deep" (John 4:11). In response to his request for a drink, she drew from the well and gave to Him. [Manners And Customs of Bible Lands]