So, we now approach the question: how did women give birth in those days? Many Nativity scenes picture Mary and Joseph being by themselves alone, but the actual picture may be quite different.
For the Middle Eastern peasant, it is a bad thing to be alone. He does his thinking in a crowd, as his culture is a group-centered one, as opposed to the individualistic thinking of the 21st century West. Thus, in the case of a birth, the men will sit apart with the neighbors, but the room will be full of women assisting the midwife, as childbirth was then the domain of women, and men did not take part in it.
In the 2nd century AD, the physician Soranus of Ephesus wrote a text on gynecology introducing the occupation of the midwife, giving us a picture as to how wealthy women in the Greco-Roman world. Soranus described her role in great detail. For example, the midwife was to have certain tools to ensure a safe delivery including: clean olive oil, sea sponges, pieces of wool bandages to cradle the infant, a pillow, strong smelling herbs in case of fainting, and a birthing stool for the delivery (in those days, women did not give birth lying down, but sitting!)
But even with the deed done, all was not over yet. According to the Law, the blood of childbirth made a woman impure, and Mary still had to undergo purification to ritually cleanse herself.
Then the LORD spoke to Moses, saying, “Speak to the children of Israel, saying: ‘If a woman has conceived, and borne a male child, then she shall be unclean seven days; as in the days of her customary impurity she shall be unclean. And on the eighth day the flesh of his foreskin shall be circumcised. She shall then continue in the blood of her purification thirty-three days. She shall not touch any hallowed thing, nor come into the sanctuary until the days of her purification are fulfilled.
‘But if she bears a female child, then she shall be unclean two weeks, as in her customary impurity, and she shall continue in the blood of her purification sixty-six days.
‘When the days of her purification are fulfilled, whether for a son or a daughter, she shall bring to the priest a lamb of the first year as a burnt offering, and a young pigeon or a turtledove as a sin offering, to the door of the tabernacle of meeting. Then he shall offer it before the LORD, and make atonement for her. And she shall be clean from the flow of her blood. This is the law for her who has borne a male or a female.
‘And if she is not able to bring a lamb, then she may bring two turtledoves or two young pigeons—one as a burnt offering and the other as a sin offering. So the priest shall make atonement for her, and she will be clean.’”But that's a topic for another time. ;)
Once again, let's note two small things here: one would be that while countless Christmas pageants and artistic recreations of the birth of Jesus show Mary in labor at the very same day/night they arrive in Bethlehem (Catherine Hardwicke's 2006 film The Nativity Story is a good recent example of this), there is no indication from the Scriptural text alone that Mary went into labor at the very same day. All that Luke says of it is that it happened "while they were there", which could also suggest some time passing before Mary actually delivered her Child.
The final thing I'd like to relate is the story of the midwife Salome, found in the Protoevangelium of James and some other apocryphal gospels, still commemorated in every Eastern icon of the Nativity (cf. some of the pictures above), though she has long vanished from most Western depictions. I could do no better but merely quote it:
And I [Joseph] saw a woman coming down from the hill-country, and she said to me: "O man, where are you going?" And I said: "I am seeking a Hebrew midwife." And she answered and said to me: "Are you of Israel?" And I said to her: "Yes." And she said: "And who is it that is bringing forth in the cave?" And I said: "A woman betrothed to me." And she said to me: "Is she not your wife?" And I said to her: "It is Mary that was reared in the temple of the Lord, and I obtained her by lot as my wife. And yet she is not my wife, but has conceived of the Holy Spirit."