A good way to approach this is to think about different characters that have conflict, and think about what they might be fearful of. For example, think of the Reverend Parris. He clashes with many different people in the town; however, his conflict is born from the fear that the townspeople are going to rise against him and kick him out of the ministry. Right off the bat he reveals this fear when he is speaking he Abby. He states,
"Abigail, do you understand that I have many enemies?...There is a faction that is sworn to drive me from my pulpit."
Later, he argues with some of those very people, John Proctor and Giles Corey, about something as trivial as salary and firewood. But at its heart, he knows that Proctor dislikes him, so he picks fights because he is defensive.
Then, there is the conflict between John and Elizabeth Proctor. She still holds resentment in her heart because of his affair; she is afraid that Abby still holds power over him, and that he still cares for her. She states, during an argument over him going into town,
"John, if it were not Abigail that you must got o hurt, would you falter now? I think not."
She is afraid that he still cares for Abby, and that his feelings for her are keeping him from loving her, and doing what's right for the town. They have a lot of conflict over this situation, and at its heart is Elizabeth's fear of rejection, and John's fear that he has not forgiven him. He states to her, "look sometimes for the gooness in me, and judge me not," revealing his fear that she hasn't forgiven him.
Later in the play, Abby is afraid that the judges believe she is an adulteress, and that Mary Warren is going to be believed; so, she creates the conflict of Mary's spirit being in the room to attack her. When the judge asks her about the adultery, she shows her fear with her defensive answer: "What look do you give me? I'll not have such looks!" and later on turns on Mary. Mary, out of fear of being called a witch, turns on John and calls him a "Devil's man!" which brings in the conflict of John being accused.
These characters, and many more, are often motivated by fear, which leads to much of the conflict in the play. I hope that helps!