How did The Crucible start and end?
That depends on if you are referring to the play as written by Arthur Miller or the 1996 film adaptation. They both end the same way, but the movie begins by showing the girls "sporting" in the woods. The actual text starts after that incident. The text begins with Reverend Parris kneeling beside his daughter's bed.
As the curtain rises, Reverend Parris is discovered kneeling be-side the bed, evidently in prayer. His daughter, Betty Parris, aged ten, is lying on the bed, inert.
He is praying over her, because she has been sick, and the doctor can find no natural causes. Reverend Parris doesn't catch on to the veiled hint, so Susanna drops a big, blatant hint.
Susanna: Aye, sir, he have been searchin’ his books since he left you, sir. But he bid me tell you, that you might look to un-natural things for the cause of it.
By "un-natural" causes, Susanna is talking about witchcraft. She isn't the only person that suspects witchcraft. Abigail Williams enters very shortly after Susanna leaves and confirms the witchcraft suspicions.
Abigail: Uncle, the rumor of witchcraft is all about; I think you’d best go down and deny it yourself. The parlor’s packed with people, sir. I’ll sit with her.
From there, the witchcraft ball gets rolling very quickly. Abigail and a bunch of other girls start accusing people of witchcraft left and right.
The end of the play is crazy emotional. John Proctor is about to be hanged, but before he gets taken, he is allowed to speak to his wife, Elizabeth. John tells her that he is thinking about confessing to witchcraft in order to save his life. He knows that it is a lie, but he is willing to confess the lie in order to live, be a good husband, and be a good father. John convinces himself to confess, and confesses to the judges; however, the judges want his confession written, signed, and hung on the church door. John can't bear to have his name taken and used against the other townsfolk who are dying because they will not confess the lie.
Proctor, with a cry of his whole soul: Because it is my name! Because I cannot have another in my life! Because I lie and sign myself to lies! Because I am not worth the dust on the feet of them that hang! How may I live without my name? I have given you my soul; leave me my name!
John rips up his confession and gets led off to be executed along with several others. The play ends.