If is often the tradition to have a small concert before Christmas in children's schools to teach them the Nativity Story of Jesus. With different variations to the story if often goes something like this:

1. Joseph and Mary had to go to Bethlehem.
2. Mary went into labour before they could reach an inn at Bethlehem (according to The Nativity Story movie)
3. Because they were late (already night), Joseph could not find no inn that is available (according to The Nativity Story movie)
4. Out of desperation, Mary gave birth to Jesus in a stable between all the animals.

Then some time later during that same night:

1. Some time later that night angels appear to shepherds in the field during night.
2. Angels appear to the shepherds who were sleeping in the field with their sheep.
3. The angels sing some Christmas Carol songs usually worshipping Jesus.
4. The shepherds also go to the stable to pray to the baby (as seen in many paintings).

Then some time before or after the shepherd's story:

1. A star appear in the sky.
2. 3 rich wise men, named Gaspar, Melchior, and Balthasar, see this star and based on some prophecy they know this means that Christ was born. They follow this star.
3. They meet the baby Jesus also at the stable during the same night that Jesus was born.
4. They worship the baby (which various from kneeling to praying to the baby).
5. Each wise man gives his gift to the baby Jesus.

This concert is mixture different events in the Bible as if it all happened during the same night:

The stable story

Luke's version:

And it came to pass in those days that a decree went out from Caesar Augustus that all the world should be registered. This census first took place while Quirinius was governing Syria. So all went to be registered, everyone to his own city.

Joseph also went up from Galilee, out of the city of Nazareth, into Judea, to the city of David, which is called Bethlehem, because he was of the house and lineage of David, to be registered with Mary, his betrothed wife, who was with child.

So it was, that while they were there, the days were completed for her to be delivered.

And she brought forth her firstborn Son, and wrapped Him in swaddling cloths, and laid Him in a manger, because there was no room for them in the inn.

Luke 2:1-7 (NKJV)

Comments:

1. Joseph and Mary first went to Bethlehem and while they were there, her "days were completed" for her to delivery Jesus. Not along the way to Bethlehem.
2. Luke does not state the reason why there were no room for them in the inn. Also note that the word "inn" simply means a place where quests could stay during a trip. It is not necessary a commercial holiday accommodation where every guest gets a private room. It could be that all the guests shared a common room and Mary was simply looking for a privacy to give birth; it could be that the place was overpopulated and there were physical no space; it could be that the inn owner does not want to accommodate a woman in labour. It is all wild guesses and this detail was not recorded.
3. There are also no proof that Jesus was born in the same inn's stable. In those days people also kept animals in caves, or lower parts of buildings.
4. There are also no evidence that Jesus was born between the animals. Perhaps they cleared and cleaned the stable first (or where ever it was). First births usually takes time. If Joseph and Mary was already in Bethlehem it could mean that they had enough time to clean the manger first. Giving birth in an unhygienic stable between dirty animals make little sense.

The shepherd story

Luke's version:

Now there were in the same country shepherds living out in the fields, keeping watch over their flock by night. And behold, an angel of the Lord stood before them, and the glory of the Lord shone around them, and they were greatly afraid.

Then the angel said to them, “Do not be afraid, for behold, I bring you good tidings of great joy which will be to all people. For there is born to you this day in the city of David a Savior, who is Christ the Lord. And this will be the sign to you: You will find a babe wrapped in swaddling cloths, lying in a manger.”

And suddenly there was with the angel a multitude of the heavenly host praising God and saying:

“Glory to God in the highest, and on earth peace, goodwill toward men!”

So it was, when the angels had gone away from them into heaven, that the shepherds said to one another,

“Let us now go to Bethlehem and see this thing that has come to pass, which the Lord has made known to us.”

And they came with haste and found Mary and Joseph, and the babe lying in a manger.

Now when they had seen him, they made widely known the saying which was told them concerning this child. And all those who heard it marveled at those things which were told them by the shepherds. But Mary kept all these things and pondered them in her heart.

Then the shepherds returned, glorifying and praising God for all the things that they had heard and seen, as it was told them.

-- Luke 2:8-20 (NKJV)

Comments:

1. Commonly it is believed that Mary gave birth at night because the of the verse the shepherds were "keeping watch over their flock by night.". However, nothing suggest that the angels appeared to the shepherds the moment Jesus was born. Even the angel announced "this day" which could imply earlier that same day. Potentially the angels gave Mary and baby Jesus some time to rest after the birth, or they gave the shepherds a chance to secure their sheep so that they could have the shepherd's attention.
2. The angels praised "God in the highest" (not worship baby Jesus)
3. When one is in haste, you do not bring all your slow sheep with you like we see in the children's tales. Mostly likely the arranged someone to look after the sheep and went without the sheep, but again this detail was not recorded and is only speculation.
4. There are no evidence that the shepherds worshipped Jesus like a God as often depicted in paintings. The bible only says they "found" him and they "seen" him.
5. The purpose of their visit was not to worship Jesus, but to testify what they had seen, because "Mary kept all these things ... in her heart".
6. When the shepherds returned (not from Jesus' manger - it was after testified to different people), they glorified and praised "God" not the baby.

The wise men story

Matthew's version:

Now after Jesus was born in Bethlehem of Judea in the days of Herod the king, behold, wise men from the East came to Jerusalem, saying,

“Where is he who has been born King of the Jews? For we have seen his star in the East and have come to worship him.”

When Herod the king heard this, he was troubled, and all Jerusalem with him. And when he had gathered all the chief priests and scribes of the people together, he inquired of them where the Christ was to be born. So they said to him, “In Bethlehem of Judea, for thus it is written by the prophet:

‘But you, Bethlehem, in the land of Judah, Are not the least among the rulers of Judah; For out of you shall come a Ruler Who will shepherd My people Israel.’ ”

Then Herod, when he had secretly called the wise men, determined from them what time the star appeared. And he sent them to Bethlehem and said, “Go and search carefully for the young child, and when you have found him, bring back word to me, that I may come and worship him also.”

When they heard the king, they departed; and behold, the star which they had seen in the East went before them, till it came and stood over where the young child was. When they saw the star, they rejoiced with exceedingly great joy. And when they had come into the house, they saw the young child with Mary his mother, and fell down and worshiped him. And when they had opened their treasures, they presented gifts to him: gold, frankincense, and myrrh.

-- Matthew 2:1-11 (NKJV)

Comments:

1. The names or number of wise men is not recorded by Matthew. It could be 3, but it could also be 2 or more than 3. We only know it was more than 1. Because the wise men presented 3 gifts, the tradition is that each wise man present his own gift, however that does not rule out that perhaps together they presented 3 gifts. They were the "wise men" not the "rich men".
2. Note that Herod send the wise men to Bethlehem, but the star lead them possibly somewhere else. This means Jesus was not in Bethlehem by the time the wise men arrived as Joseph and Mary had already returned to Nazareth after her purification (Luke 2:39). This could also probably explain why Herod could not find Jesus himself and had to rely on the wise men.
3. It also does not say that the wise men arrived at the same night. The journey to follow some "star" could have take days or weeks. That is probably why Herod was willing to wait up to 2 years for the wise men to return (Matthew 2:16).
4. Matthew does not say "babe" like Luke. By the time the wise men got to Jesus, he was a "young child".
5. The wise men "come into the house" of Jesus (not the stable).
6. They "fell down and worshiped him" like a king. (Not pray to him like we often see in paintings).

This was probably necessary to supply Jesus' parents with the portable wealth to be able to flee Bethlehem and to make a living in Egypt:

Now when they (the wise men) had departed, behold, an angel of the Lord appeared to Joseph in a dream and said, “Rise, take the child and his mother, and flee to Egypt, and remain there until I tell you, for Herod is about to search for the child, to destroy him.”

And he rose and took the child and his mother by night and departed to Egypt and remained there until the death of Herod.

This was to fulfill what the Lord had spoken by the prophet, “Out of Egypt I called my son.”

-- Matthew 2:13-15 (ESV)

But Luke recorded:

And at the end of eight days (after Jesus was born), when he was circumcised, he was called Jesus, the name given by the angel before he was conceived in the womb.

And when the time came for their purification according to the Law of Moses, they brought him up to Jerusalem to present him to the Lord (as it is written in the Law of the Lord, “Every male who first opens the womb shall be called holy to the Lord”) and to offer a sacrifice according to what is said in the Law of the Lord, “a pair of turtledoves, or two young pigeons.”

And when they had performed everything according to the Law of the Lord, they returned into Galilee, to their own town of Nazareth. And the child grew and became strong...

-- Luke 2:39-40 (ESV)

This means that some time must have passed between Jesus' birth and the wise men's appearance. It must be less than 2 years, probably only a few months, because that was the age Herod determined (Matthew 2:16), and it must be more than 40 days for Mary's purification.