Arthur Miller used the Salem Witch Trials as inspiration for his play The Crucible. He exaggerates many details to exemplify his point.
In an article he wrote in 2000 called "Are You Now or Were You Ever," he compares his experiences in the 1950s with the Red Scare and the McCarthy trials and notes that
"I spent 10 days in Salem courthouse reading the crudely recorded trials of the 1692 outbreak, and it was striking how totally absent was any sense of irony, let alone humour. I can't recall if it was the provincial governor's nephew or son who, with a college friend, came from Boston to watch the strange proceedings. Both boys burst out laughing at some absurd testimony: they were promptly jailed, and faced possible hanging" (Miller).
Here, Miller notes that while he did extensive research it was supposed to be modeled after the hysteria of the time period, not on the facts of the trials. He goes on to make thematic parallels in his article not specific relationships between the facts.
Because we don't really see a trial take place on stage, I can't say whether they were accurate. He does note that the girls go and have hallucinations in court and Abigail seems to be their ring leader. However, in the real cases, often times it was townspeople who would accuse the witches not just the young girls. The "afflicted" were all ages and sexes. The magistrates were more than just Sewall, Danforth & Hathorne. There had to be five magistrates present to move forward with the proceedings. Reverend Hale would have had no business signing death warrants. He was a member of the clergy not of the law.
In addition, Abigail was much younger than in the play, and John Proctor much older. At the end of the play, Nurse, Proctor and Corey all hang on the same day but that was not the case historical Salem.
You can access the transcripts of the trial on the etext.virginia.edu site as sourced below, and do more research on the actual proceedings of the courts there.