Explain how tone, actions, and words were used by the characters to display racism in To Kill a Mockingbird?

Mrs. Dubose's words demonstrate racism in To Kill a Mockingbird. One day Scout and Jem are walking into town. Jem, who recently celebrated his birthday, agrees to buy Scout a baton. Mrs. Dubose begins to interrogate the children with questions about where they are going and what they are doing. She insists that the children are up to no good, and she proposes that Scout will never be able to accomplish anything more than "waiting for tables at the O.K. cafe" if she does not change her behavior. Jem and Scout maintain their composure despite Mrs. Dubose's verbal attacks toward them.
However, Mrs. Dubose directs her next attack at Atticus Finch, their father. This upsets Jem far more (and leads him to take his anger out on Mrs. Dubose's flower garden a bit later). Mrs. Dubose says to the children,

"Not only a Finch waiting on tables but one in the courthouse lawing for niggers! . . . Yes indeed, what has this world come to when a Finch goes against his raising? I'll tell you! . . . Your father's no better than the niggers and trash he works for!" (ch. 11)

While this scene expresses Mrs. Dubose's disapproval of Atticus Finch's choices, it also reveals her immense racism. She believes that it is morally wrong for Atticus to defend an African American man. She says that this behavior is "against [Atticus's] raising." Additionally, she equates dark-skinned people with trash and suggests that Atticus must also be trash for defending Tom Robinson.
A significant action in the book that reveals racism is seen in chapter 15 when Heck Tate and several other men come to see Atticus after hearing rumors of possible trouble when moving Tom Robinson to the county jail. When the men arrive, Jem asks Heck Tate and his companions if they want to come inside. They refuse his offer but want Atticus to go outside to talk to them. This refusal shows the distance between Atticus and these men. The men do not want to be closely associated with Atticus and his family at this moment. Soon later, Mr. Link Deas, another visitor, explains his thoughts:

"—don't see why you touched it [the court case] in the first place. . . . You've got everything to lose from this, Atticus. I mean everything" (ch. 11).

Mr. Tate, Mr. Deas, and the other men do not understand Atticus's decision to support an African American man at court. They insinuate through their words and actions that a black person's life is worth less than a white person's life. They can't understand why he would risk the comfort and well-being of his family for Tom Robinson. Atticus contradicts this idea in his response:

"Link, that boy might go to the chair, but he's not going till the truth's told. . . . And you know what the truth is." (ch. 11)

Atticus is determined to defend Tom Robinson because he believes that Tom is telling the truth. He does not defend people because of their skin color; he seeks to promote justice, alone.