Summary: God will overthrow those who are opposed to him, his appointed leader will take his place over the people, and the rule of God will extend to the whole earth until all those who were cut off have been brought back to worship God in Jerusalem.
As we come to chs 9 & 10 of Zechariah it might be helpful to know that the book is divided into 3 parts:
1-6: Visions God says:
return to me and I will return to you
I will judge the nations
forgive your sins
raise up godly leaders
bring the nations to Jerusalem to worship
7&8: Teaching. God says:
I scattered you
I will gather you
I will bring the nations back with you
9-14: Prophecy. God says, I will:
judge the nations
punish your bad leaders
give you godly leaders
forgive your sins
reign in Jerusalem
bring all nations to Jerusalem to worship me.
Notice that each section says basically the same thing though in different ways. Notice especially, that each section ends with the same theme, of the nations coming to Jerusalem to worship. That indicates fairly clearly that this is a fairly important theme in the book, since each section ends with it.
Well, as we begin to look at Chs 9 & 10 we discover that they form a parallel. Two different prophecies with the same message. In ch 9 the prophecy is of God the warrior, while in ch 10 it’s of God the shepherd. Each chapter has three sections. The first shows God coming to overthrow those who are opposed to him, the second describes how his appointed leader will take his place over the people, and the third describes how the rule of God will extend to the whole earth until all those who were cut off have been brought back to worship God in Jerusalem.
So lets have a look at these 2 chapters.
In ch 9:1-8 we begin with God the warrior coming through the holy land from north to south and ending up in Jerusalem. If you’d been in our Tuesday night bible study recently, you might notice a resemblance between these verses and the description in Joshua 10 & 11 (quickview)  of the initial conquest of the land. God the warrior will begin in Hadrach, Hamath and Damascus in the north, then he’ll work his way south via Tyre and Sidon, down to the Philistine cities of Ashkelon, Gaza, Ekron and Ashdod, until he comes to Jerusalem.
He’s coming through the land, ending up at Jerusalem to defend his house, the Temple and in the process, defeating the enemies of God’s people. But it isn’t just destroying his enemies, notice. Have a look at v7: "I will make an end of the pride of Philistia. 7I will take away its blood from its mouth, and its abominations from between its teeth; it too shall be a remnant for our God; it shall be like a clan in Judah, and Ekron shall be like the Jebusites." Although God is conquering his enemies, some of them will turn away from their idol worship to worship the true and living God, just as the people of Jerusalem had done, when the Israelites first came into the land and they too will be incorporated into the people of God.
Then in ch 9:9 we find these words that are so familiar from the NT: "Rejoice greatly, O daughter Zion! Shout aloud, O daughter Jerusalem! Lo, your king comes to you; triumphant and victorious is he, humble and riding on a donkey, on a colt, the foal of a donkey." Here we have this wonderful picture of God’s anointed king entering Jerusalem, triumphant, yet humble, to bring in the reign of God, to bring peace, an end to war, to the whole world, because his rule will cover the whole world.