Scout learns a number of lessons as a result of Tom Robinson's trial, from the lead-up to the trial to the trial's aftermath.
The first, specific change that is demanded of her because of the trial is a greater restraint. Scout's cousin, Francis, mocks her because Atticus is prepared to defend Tom Robinson in court. Francis repeats things he has heard in his house to the effect that Atticus is ruining the family. Scout responds by punching Francis.
This episode leads Atticus to make a new demand on Scout - to hold her head high and refuse to retaliate to insults. Though learning to hold back from a fight takes time for Scout, she develops remarkably with time.
By the end of the novel, however, eight-year-old Scout has learned a measure of restraint, primarily through the influence and example of her father Atticus.
The social pressures of the trial lead Scout to learn this lesson of restraint and also lead to further lessons about justice. The night before the trial, Scout defuses a mob and comes to realize that people are capable of doing each other great harm.
She becomes aware that not everyone acts with good intentions and becomes exposed to racism, bigotry and violence.
The trial itself teaches Scout about what it means to accept one's duty to do the right thing, regardless of the outcome. Atticus loses the case but adheres throughout to his principles. After the verdict is handed in he does not cry or pout or become dejected.
This example along with other experiences surrounding the trial help Scout to mature into a more accurate perspective on proper behavior and on the nature of her community.