There are many things in the novel that speak of injustice. Let me name a few of them for you.
First, the most blatant and powerful form of injustice concerns race. It is apparent that Tom Robinson is innocent. All the evidence points in this direction, but he is still seen as guilty. This shows injustice. The following is a powerful quote on this topic:
Then Mr. Underwood’s meaning became clear: Atticus had used every tool available to free men to save Tom Robinson, but in the secret courts of men’s hearts Atticus had no case. Tom was a dead man the minute Mayella Ewell opened her mouth and screamed.
There is also injustice in the treatment of Boo Radley. People judge him and assume things about him, even though he is a good person. Also when we consider his upbringing, it is clear that he is not treated well. At times parents do not treat their children well.
These two examples should get you started.
The theme of injustice is the binding factor in the plot of To Kill a Mockingbird. As a result, it is also a motif that is presented in different versions such as discrimination due to race, class, educational background, religious denomination, family name, and family history.
A very powerful quote found in chapter 20 helps to answer the question of what creates injustice. The first part of the quote, as spoken by Atticus, reads:
[Mayella] has committed no crime, she has merely broken a rigid and time-honored code of our society, a code so severe that whoever breaks it is hounded from our midst as unfit to live with.
Here is the first factor that creates injustice: those "time-honored and rigid" codes of conduct can become very dangerous, especially when they are left stuck in time without being questioned or revisted.
The "time-honored and rigid" code that Atticus is talking about is the anachronistic tradition of separating blacks from whites in all aspects of life. In Maycomb, this code is treated as a rule even though the rule is unethical, unfair, and inhumane. It seems crazy that 1930s Maycomb would continue to hold true to that tradition even 65 years after the 13th amendment was passed in Congress, abolishing slavery. Yet this is possible thanks to ignorance combined with malice.
Ignorance and malice are further indicators of injustice. Malice can feed off ignorance and vice versa. Committing an inhumane act and using ignorance or poverty as an excuse reflect evil intentions. That is exactly what Bob Ewell does. About this, Atticus says in the second part of his quote:
She [Mayella] is the victim of cruel poverty and ignorance, but I cannot pity her: she is white. She knew full well the enormity of her offense, but because her desires were stronger than the code she was breaking, she persisted in breaking it.
In other words, Mayella acted upon sexual impulse, loneliness, and the willingness to lie even in a court of law. Her father acted upon his desire to blame a scapegoat for what he does to his daughter, and his desire to ruin a man's life. We find that Ewell continues his evil rampage well after the trial, even going as low as trying to attack the Finch children.
The question of how to overcome injustice is nearly impossible to answer in a formulaic way that could help us either avoid it or tolerate it. When the grievance involves friends or family members, injustice is nearly impossible to overcome. For example, you would want justice if someone assaulted, insulted, or showed other types of unjust behavior to your parents, or to your closest friend. Certainly you would want to do something about it, or would feel angry about the unfairness of the act. At some point, however, you have to deal with your emotions, get counseling, and find a way to vent your frustration that does not involve self-sabotage.
Injustice is painful at every level, and is one of those things that about which it is difficult to find closure, even when we avenge or bring justice to the victim. For this reason some people resort to meditation, prayer, and even avoiding specific people all together; the least we can do is control our side of the fence the best way we see fit.