Before we get to your question about Arthur Miller's The Crucible, let us first look at the definition of your chosen term (provided here by Carson-Newman University):
PATHOS (Greek, 'emotion'): In its rhetorical sense, pathos is a writer or speaker's attempt to inspire an emotional reaction in an audience—usually a deep feeling of suffering, but sometimes joy, pride, anger, humor, patriotism, or any of a dozen other emotions...In its critical sense, pathos signifies a scene or passage designed to evoke the feeling of pity or sympathetic sorrow in a reader or viewer.
It helps to think of Abigail Williams as the author of her very own play-within-a-play. She performs for the crowd using pathos to "evoke the feeling of pity or sympathetic sorrow." This occurs many times throughout the play; she feeds off the emotions of those around her in order to manipulate them. In the case of The Crucible, the most prevalent emotion is that of fear—fear of witchcraft and fear of accusation.
After being caught dancing in the forest late at night with a group of friends, Abigail confesses that there is nothing untoward going on: "Uncle, we did dance; let you tell them I confessed it. But they're speakin' of witchcraft; Betty's not witched." When she sees the adults around her getting worked up over the possibility of witchcraft, she then blames everything on "Tituba and Ruth." Knowing, as Betty explains a short time later, that she "drank blood" that night, she knows there might be grave repercussions for those actions. Thus, when Betty continues to mention it, she uses Pathos for the first time:
ABIGAIL: [...] Now look you. All of you. We danced. And Tituba conjured Ruth Putnam's dead sisters. And that is all. And mark this-let either of you breathe a word, or the edge of a word about the other things, and I will come to you in the black of some terrible night and I will bring a pointy reckoning that will shudder you. And you know I can do it. I can make you wish you had never seen the sun goes down!
Clearly shaken by everything that has happened thus far, Betty's emotional condition leads others to enter the room. This leads Abigail to claim that it started while they were praying, which only feeds their fears of witchcraft. Though this example does not directly answer your question, it does give some background into how Abigail learns to manipulate those around her using pathos.
After Abigail's advances toward John Proctor—a man with whom she was previously engaged in an affair—are rebuffed, she begins setting her sights on Elizabeth, his wife: "She is blackening my name in the village! She is telling lies about me! She is a cold sniveling woman and you bend to her!" Here, Abigail uses pathos to win John's affections. When that doesn't work, the begins to employ a much stronger plan.
While it is not shown in the play, Abigail's strongest use of pathos comes when she (presumably) stabs herself in the stomach with a needle. Ezekiel Cheever, a clerk of the court, explains what happened:
CHEEVER: The girl, the Williams girl, Abigail Williams, sir. She sat to dinner in Reverend Parris' house tonight, and without word nor warnin', she falls to the floor. Like a struck beast, he says, and screamed a scream that a bull would weep to hear. And he goes to save her, and stuck two inches in the flesh of the belly he draw a needle out. And demandin' of her how she come to be so stabbed, she... (To Proctor) testify it were your wife's familiar spirit pushed it in.
Now, most people would have a tough time believing Abigail would have done this to herself. Without knowledge of her affair with John or her attempt to get him to leave his wife, Abigail would seem like an innocent victim—even with the absurd claim that Elizabeth's "spirit" was the perpetrator. However, by this point in the play it has been shown that Abigail will go to great lengths to gain John's love, so it is safe (for the audience) to assume she stabbed herself and used the town's fear of witchcraft to try to get rid of Elizabeth.
Throughout the play, Abigail employs pathos in her behavior toward just about every other character in the play. For further study you can look into Abigail's behavior in court, where she employs pathos when she turns on Mary—who has testified on Elizabeth's innocence. Additionally, you can explore the beginning of the play, where she also turns on and blames Tituba for the events in the woods.