How is Abigail Williams manipulative?
When Mr. Hale questions Abigail during Act One, it becomes apparent that she is about to be blamed for Betty's illness and that she could be blamed for something even worse: inviting the Devil into Salem. He accuses her of concealing information, and, in the next moment, when Tituba enters the room, Abigail immediately accuses Reverend Parris's slave of forcing her and Betty to drink blood. She says, "She made me do it! She made Betty do it!" Surely, Abigail is aware that her word will be taken over a slave's and that this would be a good way to take some of the heat off of herself. Such a move is manipulative.
After Hale questions Tituba for a bit, Tituba gives him the confession for which he's been hoping, and he praises her highly for being "chosen to help [them] cleanse [their] village," and he promises that God will protect her. Abigail, seeming to sense an opportunity to be similarly praised, begins to accuse others of witchcraft, following Tituba's lead. She screams, "I want to open myself! I want the light of God, I want the sweet love of Jesus!" She confesses to straying from God and desiring to return to him. In this scene, then, we see Abigail deny participation in witchcraft and accuse Tituba in order deflect blame from herself; then we see her admit to what she formerly denied and use this admission to accuse others: manipulative, indeed!
In Act Two, Mary Warren gives Elizabeth Proctor a poppet that she'd made in court. Mary had stuck a pin into the poppet's stomach for safety, and Abigail had seen her do it. That night, at dinner, Abigail screamed, "And [Parris went] to save her, and, stuck two inches in the flesh of her belly, he draw a needle out." Abigail then claimed that it was Elizabeth's specter that pushed it into her stomach (knowing that Mary had taken this poppet home to the Proctors' house where it could be found and seem to confirm Abigail's story). She knows what people will think when the poppet and needle are found in Elizabeth's house, and she manipulates others with her knowledge of the poppet and the conclusions she knows they'll draw.
Abigail begins the story in Act I by trying to manipulate all of the girls into a defense of what they were doing in the forest. She says:
Now look you. All of you. We danced... 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 rechoning that will shudder you. And you know I can do it."
This demonstrates the lengths Abigail will go to in order to achieve her purpose of remaining free from blame for what Betty is going through.
Another example occurs as John Proctor enters the scene. She tries to convince him that the two of them should remain together:
I look for John Proctor that took me from my sleep and put knowledge in my heart! I never knew what pretense Salem was... And now you bid me tear the light out of my eyes? I will not, I cannot! You loved me, John Proctor, and whatever sin it is, you love me yet! John, pity me, pity me!
In this situation, Abigail believes if she just insists on Proctor's participation, he'll give into her. She also uses many gestures of affection.
Save vengence for another question. We can only answer one at a time.