How did Baba serve as a mentor towards Amir in The Kite Runner?
Amir spends most of his life trying to live up to the larger-than-life persona of his father, Baba. Baba is a physical powerhouse as well as a man who seems to make friends at every turn, and Amir desires to be just like his father.
"... everyone would see that he was my father, my Baba... I was so proud of Baba, of us. (Chapter Three)
Baba tries to mold Amir into his own image, introducing him to soccer, taking him to Buzkashi tournaments and teaching him to fly a kite. He warns Amir not to take the words of the Mullahs too seriously, and he lectures Amir on being patient and how "There is no act more wretched than stealing." But aside from his inherited kite-flying skills, Amir fails to fulfill his father's expectations. He is useless at soccer, sickened by the bloody violence of Buzkashi, and thoroughly cowardly when bullied by Assef and his cohorts; instead of standing up to the boys as Baba would have done, Amir allows Hassan to defend him. Amir sees himself as a failure, "with me as the glaring exception" to his father's greatness.
But Amir never gives up trying to earn his father's love and approval, and following their move to America, Amir completes his education and attends college. He admires Baba's switch to a working-class father, spending long hours working in a gas station to provide for his son. He joins Baba each weekend at the local flea market, learning from Baba the trade of buying and selling used items for profit. Baba arranges the marriage of General Taheri's daughter, and Amir follows the traditional Afghan marital customs, and only after Baba's death does Amir recognize
... how much of who I was, what I was, had been defined by Baba and the marks he had left on people's lives. My whole life, I had been "Baba's son." Now he was gone. Baba couldn't show me the way anymore; I'd have to find it on my own.
The thought of it terrified me. (Chapter Thirteen)
Amir's future actions--returning to Afghanistan to find "a way to be good again"--are motivated by his desire to wipe away his sins of the past: sins that he had kept from Baba in the knowledge that they would have shamed him even further. Amir's heroic decision to return to Afghanistan to locate young Sohrab proved to be worthy of Baba's upbringing.