How did the wise men or magi find Jesus in Bethlehem or even know that He was born to be a King?
The Magi or Wise Men
The magi first appear in history in the seventh century B.C. as a tribe within the Median nation in eastern Mesopotamia. Many historians consider them to have been Semites and that the Jews and Arabs are both descendants of Noah’s son Shem. The origins of the magi are also the origins of Abram (Later, Abraham), who was called by God from Ur in Chaldea. Later, the name magi became associated with the hereditary priesthood. Because of their combined knowledge of science, agriculture, mathematics, history, their political influence continued to grow until they became the most prominent and powerful group of advisors in the Medo-Persian and subsequently the Babylonian empire. They became skilled in astronomy and astrology, but there are strong similarities between them and the Jews who would come later:
They had a sacrificial system somewhat similar to the one God gave to Israel through Moses.
They were noted for their ability to interpret dreams.
Because of Daniel’s great wisdom, and because he had successfully pleaded for the lives of the wise men who had failed to interpret the king’s dream (Dan. 2:24), Daniel came to be highly regarded among the magi (saving many of their lives!), so we’d certainly expect that the magi learned much from the Prophet Daniel about the one true God, and because so many Jews remained behind in Babylon after the Exile, refusing to go back to Jerusalem, they intermarried with the people of the east. This makes it all the more likely that Jewish messianic influence remained strong in that region, even into New Testament times. Perhaps the magi had even heard about the pagan prophet Balaam (who lived in Persia) his prophecy mentioning “a star” and “a scepter” rising out of Jacob (Num 24:17).
It should be noted that the Bible doesn’t say there were three wise men or magi. It says there were three kinds of gifts; gold, kings/royalty; frankincense (prayers): the myrrh was used as an embalming oil). There may have been more kings or wise men (likely), and this must have required a caravan of up to 60 camels or more (soldiers, servants, supplies, gifts). In God’s sovereignty, these gifts probably proved useful in Joseph and Mary’s flight to Egypt, paying for their expenses, and this escape was made necessary because Herod ordered the execution of all male children, two and under in or near Bethlehem.
During the conquests of the Chaldeans, they gathered up all of the wise men of the Medes, Persians, and all of the other nations they could find (Jews included). The king sought the cream of the crop for his own private council (Dan 1:3-4), and “Among those who were chosen were some from Judah: Daniel, Hananiah, Mishael and Azariah” (Dan 1:6). Daniel’s title was rab mag or “chief of the Magi” (Dan 5:11), so he must have left some historical records of his writings for the
Babylonians, and remember, they were also historians). One such writing may have been Daniel chapter 9 where Daniel refers to the appearance of the Messiah, and goes into very specific detail about the timing of the Anointed One’s appearance (Dan 9:21-26). We know from Scripture that Daniel was a man of prayer, and he naturally wanted to know when things would be restored, so Gabriel answered Daniel’s prayer (2 weeks later) and told Daniel not only where and when the Messiah would come, but when He would be killed (Dan. 9:25-26). The magi or wise men recognized the fact that Daniel’s point of reference was not Babylon but Jerusalem (Dan 9:16), so for the wise men, it was not a guessing game. They had to have accurate information to go on or they’d have missed Him.
As a student of prophecy, Daniel understood that according to Jeremiah’s prophecy, Israel would face seventy years of captivity. This period began in 606 B.C. when Nebuchadnezzar, king of Babylon, attacked Jerusalem. In the first year of Darius (539 B.C.), the captivity was coming to an end, and Daniel longed for the deliverance of his people, so Gabriel told Daniel, “you are to know and discern that from the issuing of a decree to restore and rebuild Jerusalem [i.e., Nehemiah, Ezra] until Messiah the Prince [in Bethlehem] there will be seven weeks and sixty-two weeks; it will be built again, with plaza and moat, even in times of distress” (Dan 9:25). Next, Gabriel tells Daniel that “after the sixty-two weeks, an anointed one shall be cut off and shall have nothing. And the people of the prince who is to come shall destroy the city and the sanctuary. Its end shall come with a flood, and to the end there shall be war. Desolations are decreed” (Dan 9:26).
This passage breaks up those seventy weeks into seven weeks and then sixty-two weeks for a total of sixty-nine weeks. Then in Daniel 9:27, the seventh week is mentioned (490 years in all). Each week is a prophetic week; each week worth seven years. This means that the seventy weeks of Daniel 9 equal 490 prophetic years (bringing us up to the time of Calvary), so even after hundreds of years, Daniel’s prophecy of the coming Messiah could have been known to the wise men, and this would explain why they were able to discern the when and where of the Messiah’s birth.
Matthew wrote that it was “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 saw his star when it rose and have come to worship him.” When Herod the king heard this, he was troubled, and all Jerusalem with him; and assembling all the chief priests and scribes of the people, he inquired of them where the Christ was to be born. They told him, “In Bethlehem of Judea, for so it is written by the prophet: 
‘And you, O Bethlehem, in the land of Judah,
are by no means least among the rulers of Judah;
for from you shall come a ruler
who will shepherd my people Israel’” (Matt 2:1-6)
Matthew was quoting the prophecy of Micah (5:2) which mentions Bethlehem. This is why “Herod summoned the wise men secretly and ascertained from them what time the star had appeared. And he sent them to Bethlehem, saying, “Go and search diligently for the child, and when you have found him, bring me word, that I too may come and worship him” (Matt 2:7-8). Then, “after hearing the king, they went on their way; and behold, the star, which they had seen in the east, went on ahead of them until it came to a stop over the place where the Child was to be found. When they saw the star, they rejoiced exceedingly with great joy” (Matt 2:9-10). What or who was this star? Was this the Shekinah glory of God that we’ve read about in the Old and New Testaments (Ex 13:21; Matt 17:5; Acts1:9, 9:3)? After some fact-checking, this star was not some tri-planetary conjunction or some hanging comet that some use to try and explain it away, because not everyone saw this star, and it wasn’t just “a star,” but rather, “his star,” meaning the Messiah’s star. And notice this star (“his star”) lead them to Jesus.
The part where it says the star came to “stop or rest over” the place where the child was is from the Greek word “histemi” and this means “stood over,” like someone standing over someone. It’s very possible the magi or wise men may have first observed the star of Bethlehem the night of Jesus’ birth, seeing it up to two years beforehand and knowing when the exact time to depart for Jerusalem would be. Either way, they found Jesus, not in stable but in a “house” (Matt 2:11), and Jesus was no baby, but likely around two years old.
The truth is that this isn’t Daniel’s or Micah’s or any other man’s prophecy. It is the prophecy of God given to man by the Spirit of God, so all glory must go to God (Psalm 115:1). He has and is working an intricately woven mosaic through the fabric of time and history. And let’s be clear: history is “His-story!” Only in the Kingdom will we see the final product and all things will make perfect sense. Until then, we know that our God is in control, and for that we can thank Him. If you haven’t trusted in Christ, then He will be your Judge (Rev 20:12-15); but if you believe in Him, and He will be your Savior and your King, bringing eternal life to all who believe (John 11:25-26).
Here is some related reading for you: Christmas Bible Verses: 20 Great Quotes 
Resource – Scripture quotations are from The Holy Bible, English Standard Version® (ESV®), Crossway Bibles. (2007). ESV: Study Bible: English standard version. Wheaton, Ill: Crossway Bibles. Used by permission. All rights reserved.