When we are first introduced to Reverend Hale, it is indirectly. We learn from other characters that he "has much experience in all demonic arts." Parris says this, only a few pages into act one (we probably don't have the same version of the play, so our page numbers will be different). So, through other characters, we learn that Hale knows a lot about "demonic arts," meaning, the ways that demons and spirits of the devil work here on earth.
When Hale enters the scene, Miller, in a lengthy aside, gives us a lot of background information on him. He says that Hale has spent a lot of time studing "the invisible world," and that he had ousted a witch in his own parish. So, he had experience identifying and calling out witchcraft. He was pleased to be called upon, and felt like his expertise was finally being recognized. He brings many books on the subject, and refers to them in his diagnosis of Betty and others. All of this information can be found nearer to the end of act one.
Reverend Hale also knows enough about the law to advise John Proctor, and others, to get lawyers to present their cases, in order to be fairly represented in court. Near the middle of act three, Hale begs Danforth to let John get a lawyer. He says,
"in all justice sir, a claim so weighty cannot be argued by a farmer...send him home and let him come again with a lawyer."
He obviously knows enough about the courts to know that lawyers represent people. Also, throughout act three, Hale demands that justice be served, and that evidence be heard, even when the judges refuse to listen to it. He is more willing to look at things objectively, and to take evidence based on facts and logic, as courts are supposed to do. Because of the theocracy that the Puritans had, religious ministers were often involved with the execution of law, and Hale had also signed his name to many people's death warrants, making them valid and final.
I hope that those thoughts helped; good luck!