The trial takes place throughout Act III of The Crucible.
Act III is critical to the drama. We end up learning so much about so many of the characters. The full extent of Abigail's power is seen in Act III. She is able to wrangle the will of the judges and the other girls. Anyone who crosses her pays the ultimate price. The trial displays her willingness to do whatever is necessary to get her way.
We see Proctor's passion in Act III. In Act I, Proctor was distant and cynical about things. In Act II, his domestic challenges occupy the center of our attention. However, we also see a bit of his change into someone who realizes that action is needed. In Act III, Proctor is intense about change. He takes an active role in the courtroom in trying to challenge Abigail and a power structure that he knows is absolutely corrupt. By the end of the Act, Proctor is completely different than the man to whom we were originally introduced.
The inhumanity of the Witch Trials are on full display in Act III. We see see innocent people such as Elizabeth Proctor, Rebecca Nurse, and Giles Corey suffer. To see people like Abigail deified as innocent and pure is another aspect of the Witch Trials that disgusts us. Act III is the point where the audience wrestles with how to approache a corrupt authority structure and the innocent people who are caught up in it.