There are two answers to this question, the first occurring near the end of act two. In this act, Elizabeth is arrested after they find a poppet (a doll) in her house that has a needle stuck into its belly. Coincidentally, just that evening, Abigail fell
"to the floor...and screamed a scream that a bull would weep to hear...and, stuck two inches in the flesh of her belly, he draw a needle out. And demandin' of her how she came to be so stabbed, she testify it were [Elizabeth]'s familiar spirit pushed it in."
So, to summarize, Abby pulled a needle out of her belly and claimed that Elizabeth's witch of a spirit stabbed her with it, through the use of some sort of voodoo doll. So, when they went to Elizabeth's house and found the poppet with the needle, they felt that it was "hard proof" of Elizabeth's guilt. Never mind that Mary Warren said that she was the one who stuck the needle in the doll and that "Abby sat beside" her when she made it, and most likely saw her put the needle there. No, such logical facts hold no sway in this situation, and Elizabeth is arrested and jailed.
Later, near the end of act three, John confesses to adultery, and Abby denies it. So, Danforth brings in Elizabeth to ask her if her husband is guilty of adultery. She tells an understandable lie and says that no, he isn't. Her denial of the adultery further support's Abby's innocence, and she is able to gain control of the courts once again.
I hope that helps a bit; good luck!