The "evidence" that the citizens of the town bring to the courts to accuse others of witchcraft is highly superstitious in nature, and based mostly on the hysterical actions of a group of girls. The first accusation is probably the most accurate; it is discovered that the girls had a pot of boiling water, with a frog in it, and so Abigail blames Tituba, saying she was conjuring spirits. Mrs. Putnam admitted earlier that she had indeed asked Tituba to conjure. So, that evidence is pretty solid: a witness tells them she asked Tituba to cast spells, and Parris saw a pot with suspicious things in it. However, Tituba soon "comes clean" by confessing, and then calls out other witches. She says the names of several other ladies, and claims that they were witches too. The girls chime in. So at first, simply saying a name was enough evidence to bring people into court.
As the play progresses, here is a list of "evidence" presented that leads to a guilty verdict on the charge of witchcraft: Goody Osburn cannot state her commandments, and Mary Warren felt sick after one of her visits; Martha Corey said that if man wouldn't feed his pigs they'd die, and then they do, Elizabeth Proctor supposedly stuck a needle in Abby's belly (clever Abby actually produces a bloody needle from her belly as evidence), and Abby and the other girls pretended Mary was an evil bird to get her to "confess" and accuse John Proctor. This, along with other hysterical manifestations from the girls' are the reasons people are condemned as witches. All they have to do is faint, or scream and panic, and it is taken as evidence that the person is a witch.
All in all it seems pretty illogical and supersitious to us; even people in Salem itself at the time found it ridiculous. Unfortunately, people's more unkind, fearful and suspicious tendencies had a voice through the trials, and as a result, people died. I hope that those thoughts helped; good luck!
It's such a religious, Puritan society, that everyone believes anyone- They don't ask for much evidence, as far as the high court goes, but it's pretty obvious that they're looking at the accusers more thoughtfully than the victims...
It's not as good as Mrs. Campbell's, lol, but I tried...:)