How has Tom Robinson taught Scout life lessons in To Kill a Mockingbird?

Tom has taught Scout that the citizens of Maycomb may not really be the "best folks in the world" after all.

What has happened to poor Tom Robinson in the Maycomb county courtroom causes Scout to realize that good does not always conquer evil; further, Tom's cruel treatment by Mr. Gilmer and the jury has also taught Scout about the racial bias that exists in her environment. Indeed, Tom has taught Scout that one may be in the right, but still may be found guilty by those in power in order to satisfy their own desires.

From her witnessing of the proceedings of the trial of Tom Robinson, Scout begins to know the adult world of Maycomb as she becomes aware that there are things about her environment which differ greatly from her earlier perceptions. For instance, from listening to some of her father's cases, she is shocked that Mayella and even her dissolute father would lie under oath, yet they are somehow afforded some credibility by the jury. In addition, the gratuitous cruelty of the Ewells toward the man who was so kind to Mayella shocks her. Yet, somehow, the Ewells are also afforded more credibility than Tom is when he testifies honestly.
Thus, the most defining lesson for Scout is the mounting proof of racial bias toward the one-armed Tom who could not possibly have beaten Mayella as charged, while a reprobate like Ewell is allowed his lie. Further, when Tom is put on the stand, he ingenuously states that he felt sorry for Mayella, who has no one to aid her at her house, and helped her by breaking up a chiffarobe. Hearing this, Mr. Gilmer counters with vitriolic innuendos about Tom's expression of pity:

"You felt sorry for her, you felt sorry for her?" Mr. Gilmer seemed ready to rise to the ceiling.

For Tom, a "colored man," to feel sorry for a white woman is an egregious social mistake because this action implies that he feels himself superior to her. 

...nobody liked Tom Robinson's answer. Mr. Gilmer paused a long time to let it sink in.

Finally, Scout learns the deeper meaning of her father's words about it being a sin to kill a mockingbird. That is, the innocent Tom is shot trying to escape from prison after his conviction that comes as a result of a trial that has been nothing less than a travesty of justice. For, while in the courtroom, Tom has learned that he has been convicted before the start of the proceedings in the "secret courts of men's hearts." Therefore, after his conviction, he despairs of any hope for winning an appeal, and out of desperation, he tries to escape and is killed, having been shot an excessive seventeen times.