I provided a link below that will lead you to a detailed summary of Act Three. I also suggest reading the actual Act from the play, because it is really well done.
In a very, very small nutshell, Proctor, Giles, Mary and Francis go the the court to attempt to help their friends who are in prison. A petition attesting to the prisoners' Christian characters only leads to the arrest of those who signed it, Giles is arrested for refusing to give a witness name (a witness who can prove Putnam is land-greedy), Proctor ends up confessing his adultery to prove Abby a fraud, and Mary Warren-while initially wanting to prove the girls a fraud, turns on Proctor and he too is arrested. It is all very frustrating, and packed with intense, nail-biting moments.