The very first Christian missionaries in all history were a couple of men named Saul and Barnabas. (We know Saul better as the Apostle Paul.) They had no pattern to go by, no methodology, no background is missionary work as such. All they had was as set of very simple instructions. Those came from Jesus and were given to all his disciples.
Go you therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Spirit: Teaching them to observe all things whatsoever I have commanded you: and, lo, I am with you always, even unto the end of the world. Amen.
They had this commission, and they had a story—a story pretty much memorized by all the disciples of Jesus. It was the story of the ministry, teachings, miracles, death, and resurrection of Jesus. And they had a theology—a very simple one—that it is through the death and resurrection of Jesus that we can be saved, we can have our sins forgiven, and we can be reconciled to God. They were to take this story to the nations—which included the Gentiles.
So they were sent on their way by the church in Antioch of Syria. I presume they were given funds, prayers, and maybe a box lunch for the first day out at sea. After that, they were on their own. You can’t help wondering what they expected as they went, but almost certainly they did not expect what actually happened. Everywhere Paul went, he went to the Jews first. (He was clear enough on the principle,
to the Jew first, but also to the Gentile.) One of the best illustrations of how this all worked is found in Acts 13, on Paul and Barnabas’ first visit to Antioch of Pisidia.