Matthew never says. The number three comes from the three gifts: gold, frankincense and myrrh. Some Eastern churches told the story with twelve. They are not called kings, they are not named, they are not at the manger, and nobody mentions camels.
Matthew 2:1–12 is the only place they appear.
Now when Jesus was born in Bethlehem of Judaea in the days of Herod the king, behold, there came wise men from the east to Jerusalem.Matthew 2:1 — "wise men" translates μάγοι, magi
And when they were come into the house, they saw the young child with Mary his mother, and fell down, and worshipped him: and when they had opened their treasures, they presented unto him gifts; gold, and frankincense, and myrrh.Matthew 2:11 — a house and a young child, not a stable and a newborn
Then Herod … slew all the children that were in Bethlehem, and in all the coasts thereof, from two years old and under, according to the time which he had diligently enquired of the wise men.Matthew 2:16 — Herod's two years suggests the visit came well after the birth
Almost every detail of the nativity scene's three kings comes from later tradition rather than from Matthew. That tradition is not foolish. The gifts suggested three, and Psalm 72:10–11 and Isaiah 60:3–6 speak of kings bringing gifts and nations coming to the light. But it is reflection on the text, not the text.
Graded by how sure it is possible to be.
The mistake is not the nativity play. It is forgetting where the text ends and the tradition starts. The tradition is old and often thoughtful, but a reader should know which is which before building anything on it.
And the detail that matters most is the one the crib scene keeps: Gentiles from far away came looking for the king of the Jews and worshipped him, while Jerusalem's own leaders, with the Scriptures open in front of them (2:4–6), stayed home.
The star. Whether Matthew is describing something astronomers could have seen, or a sign with no natural explanation, is still argued, and the answer you give tends to follow from what you already think a miracle is.