The play begins with basic exposition before the plot proper gets underway. The facts surrounding of Betty's illness are discussed and the insecure situations of Parris and Abigail in Salem are presented.
The plot begins really when Abigail and Parris are joined by the Putnam's in Betty's room. The next plot point occurs when Mary Warren arrives and the girls debate their course of action (this moment offers further exposition as well, cueing the audience to the danger the girls face and also showing Abigail's ruthless side).
More plot points in this first act include Proctor's arrival and his argument with Parris and Hale's arrival and his prognosis.
The second act features Proctor returning home to argue with Elizabeth, Mary Warren's return from the court and her announcement of Abigail's actions, Hale's arrival to the Proctor home, and Elizabeth's arrest.
The third act has Proctor and Mary Warren go to court to try to stop the trials and free Elizabeth. In this act Mary Warren is dominated and defeated by Abigail through acting and trickery. Proctor is forced to admit to his affair with Abigail. Proctor is arrested.
The final act is set in the prison. Hale tries to convince Danforth to postpone or stop the hangings that are scheduled and fails. Proctor is visited by Elizabeth. Danforth gets a false confession from Proctor then Proctor refuses to sign a written confession. Proctor is taken away to be killed.
A more detailed plot summary is available on The Crucible page.