What does the court accept as evidence that someone is a witch in The Crucible?
The previous post is good. I'd like to add that, in the historical Salem witch trials (as in The Crucible), the court admitted what they called "spectral evidence" as proof of someone's guilt. This evidence didn't have to take physical form. For example, for the judges, it was often enough that a young girl claimed that she was being pinched or tormented by the floating, non-physical form of the accused witch.
The admission of spectral evidence led to mass jailings. Cotton Mather challenged the admission of this sort of evidence, but his reasons were not like those that we mght hear today in our arguments over what is admissable evidence and what is not; Mather believed that the devil was able to impersonate innocent people and could very have been the one pinching and tormenting the young girl, for example.
A link to a brief overview is given below.
The main evidence that the court accepts for whether someone is a witch (in Arthur Miller's The Crucible) is the testimony of the girls lead by Abigail Williams. When the girls shriek or faint or get cold or pretend to see a bird, that is seen as proof.
It also appears that you can get in trouble for the sorts of things Proctor does or doesn't do -- failing to remember all ten commandments, not coming to church enough. Or what Elizabeth Proctor does -- saying that she doesn't really believe in witches.
So all in all, it really seems that the court will accept almost any evidence and use it to charge a person. At that point, if the person doesn't confess, it's proof that they are a witch and deserve execution.