In The Crucible, how does the author change history to fit his purpose?

For one, Miller brings Abigail and Proctor much closer in age than they were in real life.  The real Abigail was only thirteen (she's seventeen in The Crucible) and Proctor was in his sixties (he's in his thirties in the play).  By changing their ages, and giving them a sexual relationship, Miller begins to characterize the girls as purposeful and knowing instigators who sought, with their eyes wide open, to ruin the lives of innocent people.  

In real life, there was no dancing in the woods, conjuring dead babies, or drinking charms to kill Elizabeth Proctor.  In truth, Abigail and Betty Parris only sat with Tituba, doing a bit of old folk magic she brought with her from Barbados.  They broke an egg and spilled its white into a glass of water; the shape taken by the egg white was supposed to show them some symbol associated with the occupation of their future husbands.  When the girls saw a coffin, they began to panic.  Other girls begin to come and listen to Tituba's stories, and slowly, it seems that the children are overwhelmed by guilt and worry because they know that they are engaging in activities that that are not allowed under Puritan law.  Again, I think Miller probably made this change in order to paint the girls as completely aware of what they were doing.  It doesn't begin innocently in The Crucible as it did in life; it begins maliciously and with intention.  

It is likely that Miller wants to portray the girls in this way because the play is not simply a dramatic depiction of the Salem Witch Trials, but it also aims to skewer Senator Joseph McCarthy and the House UnAmerican Activities Committee, the group responsible for the witch hunt for Communists in the 1950s and 60s.  Miller, himself, was called to testify before the committee because he had attended a Communist meeting several years prior.  In the attempt to root out Communists, McCarthy and his cronies ruined the lives of many, employing many of the same tactics we saw in the Witch Trials and in The Crucible.  The creation of hysteria and fear was key.  The similarity in the enemy -- that the evil ones don't seem evil on the surface -- also helped to inspire paranoia.  Further, in both historical situations, the accused were expected to "name names," or identify others who were also involved in wrongdoing.  Children informed on teachers, neighbors informed on neighbors, and the hysteria spread like wildfire, taking on a life of its own.  

Miller also gives Reverend Hale a role in The Crucible that his namesake did not actually have in life.  Miller seems to use him as a representative for those who know that something unjust is occurring and do nothing to stop it.  Despite his misgivings as early as Act Two, Hale supports the court's authority and proceedings.  Then, in Act Three, instead of continuing to fight against the court he now realizes is corrupt, he simply abandons Salem to its own devices.  Later, in Act Four, his conscience compels him to return and counsel the convicted; he wants to save their lives, and he has realized his role in their destruction.  The real-life Hale did none of these things; Miller changes, him, however, to symbolize those people who question and say nothing.

Further, the real Abigail Williams did not rob Parris and board a ship with Mercy Lewis to escape the storm she caused.  Instead, she lived out the remainder of her life quietly.  Again, Miller wants to make the girls seem as culpable as possible because he is using the girls who cause the witch hysteria to represent McCarthy and the HUAC.