Explicit fulfillment
Out of Egypt
Matthew says that Jesus' time in Egypt until Herod's death fulfilled Hosea's words, "Out of Egypt I called My Son."
Hosea 11:1
When Israel was a child, I loved him, and out of Egypt I called My son.
Hosea 11:1 recalls God calling His son out of Egypt, and Matthew 2:15 quotes that line after Joseph takes Jesus and Mary to Egypt, where they remain until Herod's death.
Explicit fulfillment
Rachel weeping for her children
Matthew identifies the mourning after Herod's killing of the boys near Bethlehem with Jeremiah's words about Rachel weeping for her children.
Jeremiah 31:15
This is what the LORD says: “A voice is heard in Ramah, mourning and great weeping, Rachel weeping for her children, and refusing to be comforted, because they are no more.”
Jeremiah 31:15 speaks of a voice in Ramah, mourning and great weeping, and Matthew 2:17-18 quotes the passage after saying that what Jeremiah spoke was fulfilled.
Quotation
The ruler from Bethlehem
When Herod asked where the Christ was to be born, the chief priests and scribes cited Micah to identify Bethlehem as the birthplace of Israel's promised ruler.
Micah 5:2–4
But you, Bethlehem Ephrathah, who are small among the clans of Judah, out of you will come forth for Me One to be ruler over Israel— One whose origins are of old, from the days of eternity. Therefore Israel will be abandoned until she who is in labor has given birth; then the rest of His brothers will return to the children of Israel. He will stand and shepherd His flock in the strength of the LORD, in the majestic name of the LORD His God. And they will dwell securely, for then His greatness will extend to the ends of the earth.
Micah 5:2 says that a ruler for Israel would come from Bethlehem Ephrathah, and verse 4 describes Him shepherding His flock; Matthew 2:5-6 cites the prophet and repeats Bethlehem, the coming ruler, and the shepherding of Israel.