The pivotal characters in the play are John and Elizabeth Proctor. How are they involved in these trials?

John and Elizabeth Proctor only become involved in the witch trials because of their past relationships with Abigail Williams, the niece of Reverend Parris, who makes the initial accusation against Tituba, Parris's slave, as well as the majority of the succeeding accusations.

Abigail used to work for the Proctors, helping out in their home and with their children. She and John began to have an affair, and when Elizabeth found out about it, she fired Abigail from their service. Abigail believes that John still has feelings for her. In Act One, she says, "I saw your face when she put me out, and you loved me then and you do now!" She blames Elizabeth for separating them and for making him keep his distance from her.  

In Act Two, we learn of Elizabeth's belief that Abigail "wants [her] dead." Mary Warren, their new employee, says that Elizabeth's name was "mentioned" in the court, but she assured the judges that she never saw any reason to suspect Elizabeth of witchcraft. Elizabeth now fears that Abigail will accuse her in order to get her out of the way; "She thinks to take my place, John," she says.

Elizabeth turns out to be right, as we learn at the end of this act. In Act Three, when John goes to the court to defend her, Mary Warren turns on him and he is accused too. This is how this couple becomes involved in the trials; it all began with John's affair with Abigail.