Chapters 16 - 19 concern the trial of Tom Robinson. Almost any passage you choose that relates to the testimony of the witnesses - Bob Ewell, Mayella Ewell, Heck Tate -- are important because they illustrate the various social prejudices in the town. Even though Bob and Mayella are obviously lying, it is clear that the townspeople and the jury are going to side with them anyway, just because they are white.
In chapter 20, I think an important passage is Atticus' final statement to the court. He sums up why they should find Tom innocent, ending with:
A court is only as sound as its jury, and a jury is only as sound as the men who make it up. I am confident that you gentlemen will review without passion the evidence you have heard, come to a decision, and restore this defendant to his family. In the name of God, do your duty."
In chapter 21, Tom is convicted. I always liked the part at the end where the blacks in the balcony show their respect for ATticus and tell Scout to stand up because her "daddy is passing."
In chapter 22, I think that Miss Maudie's comments are important because they express the author's ideas and hint at the themes of the novel:
"I simply want to tell you that there are some men in this world who were born to do our unpleasant jobs for us. Your father's one of them."
She also tells the children that there is a reason that Atticus was appointed to defend Tom instead of the usual inexperienced court-appointed attorney:
"We're the safest folks in the world," said Miss Maudie. "We're so rarely called on to be Christians, but when we are, we've got men like Atticus to go for us."
In chapter 23, Atticus tells Jem that there may be hope for Maycomb because the jury took a long time to make up its mind and the last holdout was one of the Cunninghams:
"No it didn't," he said, more to himself than to us. "That was the one thing that made me think, well, this may be the shadow of a beginning. That jury took a few hours. An inevitable verdict, maybe, but usually it takes 'em just a few minutes. This time " he broke off and looked at us. "You might like to know that there was one fellow who took considerable wearing down-in the beginning he was rarin' for an outright acquittal."
Chapter 24 is a great chapter - it's the one with the missionary women. Any passage in that chapter would be great - especially anything that Miss Maudie says.
In chapter 25, Tom is killed while ostensibly trying to escape and Scout reads an editorial criticizing the senseless killing of Tom. Scout says:
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.
In chapter 26 Scout hears her teacher telling how awful Hitler is persecuting the Jews due to hateful prejudice and Scout reports that she overhead Miss Gates after the trial:
I heard her say it's time somebody taught 'em a lesson, they were gettin' way above themselves, an' the next thing they think they can do is marry us. Jem, how can you hate Hitler so bad an' then turn around and be ugly about folks right at home---"
A great example of irony!
This should give you some help. You can read about the novel here on eNotes.