Luke's account is once again very straightforward, providing succinct details and moving the story along quickly. The events probably took place around the time of the fall harvest. The evangelist informs us that Joseph and Mary traveled to Bethlehem to be registered for the tax that had been decreed by Caesar Augustus in 8 BC, but which was not levied on the Jews until 4 BC due to a Jewish revolt. Normally, registrations like this were done after the people were finished harvesting their fields so that they, first, would not be working and, second, would have the money to pay the tax. This latter reason was very important to the Romans.
The best estimate is that Jesus was begotten, as announced in Luke 1:26-38, ironically, during the end of December, and that He was born near the end of September or in early October of the following year. This means His birth occurred around the Feast of Trumpets in 4 BC. Scripture, of course, nowhere states this explicitly, but the internal evidence points to this general time.
That these events took place around the fall holy days, and that the Romans' registration was happening at the same time, indicates why "there was no room for them in the inn." Jews would have begun to travel to Jerusalem for the holy days to be there for the Feast of Trumpets, and would have remained there until the Last Great Day. Bethlehem, being only about six miles outside of Jerusalem, would probably have received much of the capital city's overflow. There were probably no rooms available for miles around.
Joseph and Mary did not have a convenient Holiday Inn or Motel 6 to pull into, so they had to go wherever they could find a place to stay. They probably ended up in a grotto, a cave behind a home or an inn, where the owner housed his or his customers' horses, donkeys, and oxen. As the text relates, Jesus' first crib was a trough for the animals. With a good cleaning and some fresh straw, this stable was probably not a bad place to stay. They were at least out of the elements and had a roof over their heads.
Many people mistakenly believe that the swaddling cloths Luke mentions are rags. It was a custom of the time to wrap a child in strips of cloth, especially the limbs, perhaps to help them to develop straight. Today's equivalent would be a receiving blanket. Swaddling cloths are not an indication of Joseph and Mary's poverty. In all likelihood, they were neither better nor worse off than the average Jew of the day.