Ammon begins teaching by assessing the current understanding of his student. Ammon begins with God, because that is a rather fundamental beginning point. Ammon would be unable to explain his power without an understanding of the God who had granted it.
For the power of this story, it is important to note King Lamoni's response. Ammon asks if he believes in God. The response is "I do not know what that meaneth." Clearly there is a cultural/religious difference between Lamanite and Nephite. Even though both peoples had begun from the same Israelite stock, there is no longer enough religious similarity that King Lamoni would even understand what Ammon meant when he said "God." This is perhaps similar to the missionaries who must serve in Asian lands where there is no word that adequately translates the concept we understand as God. King Lamoni apparently had no reference readily available. Ammon and King Lamoni are beginning worlds and cultures apart.
26 And then Ammon said: Believest thou that there is a Great Spirit?
27 And he said, Yea.
Ammon backs away from the specific question about God, and uses a term that he has heard King Lamoni use. We do not know whether or not Ammon fully understood what the King meant when he used that term, but Ammon took what he could from the concept and used it as the springboard to teaching. What Ammon is doing is creating a common base of understanding. Most teachers will find that to teach more, they must begin with less, and specifically a point where there is some commonality. The student will learn more if there is at least a beginning from some common understanding than they will if they are presented with completely foreign concepts. In this, Ammon is using a technique similar to the one Paul used in Acts 17 when he used the altar to the Unknown God as the springboard to his discussion of the Christian godhead.