The power of the Holy Ghost
In "Preach My Gospel: A Guide to Missionary Service" (which the manual used by LDS missionaries) it states (in Chapter 4)
The power of the Holy Ghost. The witness that comes to sincere investigators before baptism comes through the power of the Holy Ghost. “The power [of the Holy Ghost] can come upon one before baptism, and is the convincing witness that the gospel is true. It gives one a testimony of Jesus Christ and of his work and the work of his servants upon the earth” (Bible Dictionary, “Holy Ghost,” 704). The Holy Ghost testifies of truth. All people can know the truthfulness of the Book of Mormon through the power of the Holy Ghost. “By the power of the Holy Ghost ye may know the truth of all things” (Moroni 10:5).
This applies to both native and non-native populations that missionaries have taught or are currently teaching.
Of course, this is not the only method used by Christian missionaries throughout history. Some Churches in the past have relied on coercion, unfortunately. But sincere and lasting conversion can only come via the power of the Holy Ghost.