First things first. It is obvious, and well accepted, that the two birth stories, in the Gospels of Matthew and Luke respectively, are independent and complementary. Matthew tells the story largely from Joseph's perspective, and refers to the visit of the Magi. Luke tells it from Mary's perspective, and recounts the visit of the shepherds. A certain irony appears in this. Matthew's is the Gospel to the Jews; it assumes Jewish customs without explanation and seeks to establish that Jesus was the fulfillment of Old Testament prophesies. Luke, on the other hand, is the evangelist to the Gentiles. It would have been more logical for him to pick up the story of the visit of the Gentile Magi, and Matthew to record the shepherds, but history isn't always recorded the way we'd expect it. What both have in common is the names of the parents, the site (Bethlehem), the date (the reign of King Herod), and, of course, the virginity of the mother. These must have been part of a very early tradition. (It is interesting, too, that Mary's name in Luke's account is rendered by the correct Aramaic form, Mariám, while in the rest of the New Testament it is María. It appears both were translated before the "official" form became established.)
The source of Matthew's account is anyone's guess. With Luke's it is much clearer: it obviously comes from a source close to the Holy Family, as can be deduced from the two references to Mary keeping all those things in her heart (Luke 2:19, 51). No, it is unlikely that Luke ever interviewed Mary. He did not arrive in Palestine until about AD 58, by which time Mary would probably have been dead. Even if she were still alive, her protector, St John was nowhere around. In fact, John appears to have dropped off Luke's radar after the events of Acts 8:14, somewhere around AD 35. Luke did, however, have contact with James, the brother of Jesus.
However, it is more likely that Luke's birth story is a Greek translation of a separate, very early document, originally in Aramaic. The language of it is quite different from the rest of Luke's fluent Greek. It displays so many Semitic turns of phrase that it sounds like a section of the Old Testament. In particular, it contains what are very clearly translations of five Aramaic poems: 1:14-17. 1:32-33, 1:46-55 (the Magnificat), 1:68-79 (the Song of Zechariah), and 2:29-35 (the Nunc Dimittis). What is not often commented on is that they all involve the idea of the Messiah as a super-secular king, and say nothing about Jesus' atoning death and resurrection. Therefore, they cannot be the late products of hindsight, but must have been written before the commencement of His ministry.
However, it is not my aim to prove the authenticity of the Biblical accounts, anymore than it is to disprove them. My aim is to explain what the Bible actually says as compares to what most people think it says.
If we had nothing but Matthew's gospel to guide us, we would assume that Bethlehem was the home of Mary and Joseph. It is Luke who informs us that both originally came from Nazareth, and moved to Bethlehem at the time of the census. From this the traditional view is that they made a dash to Bethlehem when Mary was nine months pregnant, found the local inns full, and Mary went into labour in a stable. Another corollary (I think it was Luther who noticed it) was that no-one was prepared to give up his room for a woman about to give birth. This is highly unlikely.
Firstly, neither an inn nor a stable, and certainly not an ox or an ass, is mentioned in the Bible. And it most probable that the moved much earlier, Joseph, in order to escape wagging tongues in Nazareth, using the census as an excuse to transfer to the city of his ancestors. Quite possibly he had family members with whom they could stay until he got established as a carpenter. After all, it was only because of the violence with which Archelaus' reign commenced after Herod's death that caused him to go back to Nazareth instead of returning to Bethlehem (Matt. 2:22).
But what about the inn? you say. It was mentioned in Luke 2:7. Not really. The normal word for "inn" is pandocheîon, which means "all-receiving", and an innkeeper is pandocheús. Both are used in the parable of the Good Samaritan (Luke 10:34-35). However, Luke 2:7 uses katályma, which has the broader meaning of "lodging", or simply, "guestroom", as in Matt. 14:14 and Luke 22:11. The verb from which is derives possesses two contradictory meanings: "to destroy" and, possibly on the basis of breaking a journey, "to lodge as a guest". Thus, in Luke 19:7, the people murmured, "He has gone in to lodge (katalysai) with a sinful man."
Stable? it is not mentioned. We only assume it because we read that Jesus was laid in a manger. According to Kenneth Bailey, who travelled a lot among the most traditional villages of the Middle East, the people there assume he was born in a house, because traditional houses in that part of the world contain a section at the front, somewhat lower than the main (human) living area, dedicated to the domesticated animals.
If you go to the Church of the Nativity in Bethlehem, as I have, you will see that it is constructed over a cave, and you have to descend into the cave to see the site claimed as the birthplace of Christ. A church had been present on this site since at least the early second century, because in AD 135, after the failure of the Bar Kokhba revolt, the Emperor Hadrian desecrated it, converting it into a temple to Adonis, while that of the Holy Sepulchre was dedicated to Venus. It is also certain that, in the middle of the second century, the Christian writer, Justin Martyr referred to the cave where Jesus was born. Personally, I can't see how it would be possible to identify the correct site even in the first century, but is should be noted that, in Nazareth, the sites traditionally claimed to have been the homes of Joseph, and of the Virgin Mary before her marriage, were both caves. Although the authenticity of each may be seriously questioned, there does appear to have existed very strong traditions of caves used as homes.
To the extent that the Church of the Nativity is accurate, the cave may have been the stable for an inn or private dwelling above. Or the whole dwelling place of people and animals may have been below ground. But where would the birth itself have taken place? All the Bible actually says (Luke 2:7) is: "[She] laid him in a manger, because there was no place for them in the katályma." That might simply mean that there no opportunity for privacy in the rest of the lodgings when the hour of childbirth arrived. In those days people used inns only when they had no friends or relatives in the area, because they were not exactly salubrious places. We shouldn't assume they were divided up into rooms or cubicles. There certainly wasn't any room for such in the cave under the modern church.
Next we have the visit of the Magi. Traditionally, it has been assumed there were three, because of the three gifts, but this does not necessarily follow. People have sought to read special significance into the gold, frankincense and myrrh, but they were most likely chosen simply because of their value. As far back as the second century, the visitors have been called kings, but this is absurd. Kings do not travel singly. The come with large retinues, and make special arrangements beforehand for a state visit to the local potentate.
In fact, there is no real difficulty identifying them. They were not kings, but priests. Although magos is the normal Greek word for a magician (it is used that way in Acts 13:8), this is because the original magi practised magic. The magi were - and still are - the priestly caste of Zoroastrianism, which was the state religion of Iran before the Muslim conquest. A few Zoroastrians still remain in Iran, but most of them fled long ago to India, where they are known as Parsees ("Persians"). They form a highly prosperous community centred on Bombay, but their numbers are gradually diminishing, and Zoroastrianism is the one major world religion most likely to go extinct. (I once met an Indian lady who said she was a Christian Parsee. The second term was obviously used as an ethnic rather than a religious designation.)
Now, Zoroastrians are dualists. They believe that the world is a battleground between a good god, Ahura Mazda (Ormazd) and an evil god, Angra Mainyu (Ahriman), and that in the last days a saviour known as the Saoshyant ("benefactor") will arise to lead the human race against the forces of evil. This, then, was the one the Magi were seeking. Also, the Magi were astrologers. (And still are; in Anna and the King of Siam, Anna Leonowens had her stars read by a Parsee.)
European painters have had problems depicting these people. Mostly, as with my Christmas crib, Jews are dressed as Arabs, and the Magi as Turks. However, contemporary relief carvings show them as typical Persians. They wore trousers, and what is known as a "Phrygian cap". Also, there is one bit of trivia which is always overlooked. Zoroastrians believe that anything which comes out of a person is "dead", and therefore unclean, and that includes breath. Even today the magi wear veils to prevent their breath contaminating the sacred fires. It is a very ancient custom; relief carvings dating before Christ show them wearing veils while attending to the sacrifices. I thus find it interesting to imagine the "wise men" with veils over their lower faces as they presented their gifts to the baby Jesus.
But the biggest mistake of the Christmas crib is to have the Magi there with the shepherds on the night of Jesus' birth. Of course, it didn't happen that way! Luke 2:22 reveals how they presented Him at the Temple for the purification ceremony which the Law required, forty days after the birth of a male child (Leviticus, chapter 12). Do you think Mary and Joseph would have headed back to Jerusalem if they had known that Herod was planning to kill the boy? No, the Holy Family was well and truly settled in Bethlehem by the time the Magi arrived, and probably intended to stay there.
When did it happen? One thing that is certain is that Dionysius Exiguus, the monk who originated the Christian calendar, miscalculated the date of the birth of Christ. Herod the Great died shortly after a partial eclipse of the moon in the early hours of 13 March 4 BC. By that time he was paranoid about the throne, and had even given an order - not carried out by his heir - for a wholesale slaughter of notable citizens so that people would mourn his death. Now, the ancient Chinese recorded that a new star, probably a nova, appeared some time between 10 March and 7 April 5 BC, and lasted for seventy days. It used to rise about four and a half hours before dawn.
The Bible implies that the original star had disappeared by the time the Magi reached Herod, but then: "When they had heard the king they went their way; and lo, the star which they had seen in the east went before them." Now, curiously enough, Korean sources tell of a new star which appeared on 23 February 4 BC in the constellation of Aquila, and anyone standing at the South Gate of Jerusalem would have seen it over Bethlehem.
Not only that, but A. J. Morehouse, who researched this, suspects that, because the sources say it was extremely bright, it was probably a supernova. As such, it would have burnt out into a pulsar. He believes the best one which fills the bill is a pulsar with the unromantic name of PSR 1913 + 16b.
None of these data, of course, is beyond challenge, but at least they hang together. We will never know for sure, but they are worth considering.
(Linus has an interesting take on it all.)