In Arthur Miller's The Crucible, there were a couple of ways that the authorities tested the accused to ascertain if they were witches.
Goody Osburn is accused of being a witch. Mary Warren accuses her of mumbling words that later make Mary sick because Mary would not give her food when she begged at the Proctors' door. Goody Osburn says she was only saying her commandments. When asked in court to repeat them, she is unable because she does not know them. We might infer that being able to recite her commandments would prove her innocence. So she is sentenced to be hanged.
When Elizabeth Proctor is mentioned in court, Rev. Hale comes to see the Proctors. He asks them a number of questions to ascertain the state of their souls. He asks Elizabeth if she can recite the commandments:
HALE: ...then with the voice of someone administering a secret test:
Do you know your Commandments, Elizabeth?
Elizabeth knows them all and recites them to the minister. We can infer, once more, that this is a test to see if someone is a witch.
When they come to arrest Elizabeth, they search to see if she has a "poppet" (a doll). Mary Warren had given her one that she had made that day in court. Cheever collects the poppet and notices that a pin is stuck in it. When they ask Mary about the poppet, she admits that she made it while at court—that there were people there who could attest to the fact:
Let you ask Susanna Walcott—she saw me sewin' it in court. Or better still: Ask Abby, Abby sat beside me when I made it.
Sadly, it is Abigail Williams that has accused Elizabeth having had knowledge of Mary's poppet. At dinner, Abigail had a needle in her belly and accused Elizabeth's familiar spirit of attacking her and pushing the pin in.
So if one is a witch, they believe that he or she has the power to inflict damage to someone's body by practicing that damage on a doll.