How does Khaled Hosseini tell the story of The Kite Runner in chapter 12?
I am not sure exactly what you mean asking how the story is told. It is told in the first person, as the rest of the book is. Perhaps you are asking what happens in the chapter and how it fits in with the themes of the book?
The chapter involves two central events in Amir's life, his courtship of Soraya and a diagnosis of Baba's terminal illness. Amir begins with a reminiscence about the beginning of beginning of winter in Afghanistan, yelda, and ends with a reflection on courage.
Amir characterizes his pursuit of Soraya as a kind of yelda, a winter in his heart seeking the sunshine of love. His successful courtship warms his heart in a way that allows him to grow as a person and be capable of love, empathy and eventually, redemption. Also part of his growth as a person is the example of Soraya's courage, which sets him thinking about his own lack of courage in the past.
At the same time that he is learning about love and courage, Baba is dying. So, as Amir comes into the springtime of love, his father is in the winter of his life. Hosseini combines these two beautifully, with Baba setting out on the last mission of his life, to seek Soraya's hand for Amir, so Amir can live on happily after him.
For Amir, Baba's imminent death is sad, but a sweet sadness, because through his relationship with Baba since they have moved to America, we can see that Amir has gained love and appreciation for his father, the kind of growth that allows him to fall in love with Soraya, and be able later on in the story "to make things good again" (2). Baba's death seems like it will be the last link to his past. We know, of course, because of how the book opens, that it is not.
So, this chapter gives us love, death, sunshine and winter, all helping to set the stage for the story's eventual denouement. Did Hassan deliberately place this chapter in what appears to be almost the exact middle of the book? It's an interesting thought.