In Act Two of The Crucible, we see some key figures arrested for witchcraft; among them are Elizabeth Proctor, Martah Corey, and Rebecca Nurse. Each arrest was accompanied with "evidence" that the courts used to justify the arrest.
In the case of Goody Proctor, in her house they found a doll with a needle stuck in its belly. Coincidentally, just that evening, Abby had fallen to the ground and pulled a needle out of her belly, claiming Elizabeth's spirit had pushed it in. Now, as rational human beings, we as the readers know that Mary Warren gave that doll to Elizabeth, and, as Mary confessses later, she was the one to put the needle there. We know Abby wants John, and saw Mary put the needle there and took the opportunity to put on a little act to get Elizabeth accused. The courts, however? They took the needle as "hard proof!...I never warranted to see such proof of Hell!" as Cheever, the arresting officer tells John. So, Elizabeth is taken.
Martha Corey was arrested because she told a farmer that he needed to feed the pigs she sold them for them to live. Well, he didn't, the pigs died, and he accused her of "bewitching them with her books," so, essentially, he accused her of putting a spell on his pigs so that they would all die.
Rebecca Nurse, if you remember, was a grandmother who Ann Putnam expressed jealousy for in Act One. Ann had lost most of her babies as infants, and was jealous that Rebecca's children and grandchildren had all lived. Well, it just so happens that in Act Two Rebecca is arrested for "the marvelous and supernatural murder of Goody Putnam's babies."
This "evidence" is, to us, clearly based in jealousy, ignorance, and revenge; John Proctor realizes this as he says to everyone:
"Why do you never wonder if Parris be innocent, or Abigail? Is the accuser always holy now? Were they born this morning as clean as God's fingers? I'll tell you what's walking Salem--vengeance is walking Salem...common vengeance writes the law. This warrant's vengeance! I'll not give my wife to vengeance!"
To the courts at the time, however, the evidence outlined in this act was enough to arrest--and eventually hang--most of these women.