In such a complex novel, it is difficult to give a summary. I will have to be selective. As I see it, there are four main points.
First, Amir, the protagonist is telling a story of what happened to him over twenty years ago when he lived in Afghanistan. They were fairly well off and they had two servants Ali and his son Hassan. Life was good.
Second, one winter there was an important kite tournament and in Amir's father, Baba, says that Amir has a good chance of winning. He actually does. As Hassan is about the fetch the kite that lost (which was a great honor), Assef and a few other boys find Hassan and demand the kite. Hassan refuses and so they rape him. Amir witnesses this, but he does nothing. This shame eats at him and he cannot bear the sight of Hassan on account of his guilt. So, he frame Hassan to get him in trouble, and they depart.
Third, there is a coup that takes place and the King of Afghanistan is ousted and the Taliban take over. This causes Baba and Amir to leave and flee to Fremont California, where they start their new lives. In time, Amir meets a girl that he falls in love with and marries her (Soraya). Rahim Khan from Kabul, an old friend, asks him to come and visit. When Amir does he learns that Hassan and his wife were killed by the Taliban and had a child Sorhab, who was now in a orphanage.
Fourth, Amir goes to get Sorhab and he meet Assef. Assef recognizes him and beats him terribly, but Sorhab uses a slingshot to wound Assef and they escape. In the end, Amir and his wife, Soraya adopt the little boy. This is particularly fitting, since Soraya could not have kids and through Sorhab, Amir is able to redeem himself.