There isn't a short answer to this question. A lot happens between February 1692 and May 1693 that is called the Salem Witch Trials. Accusations of witchcraft originated in Salem Village, present day Danvers MA, and continued to be made across Massachusetts, as far south as Boston and as far north as what is now York, ME. In total 19 people were hanged, 1 pressed to death, 5 died in jail, and 150 people were arrested. Given how long I spend speaking about what happened, I'll give you a brief timeline summary that will be much easier to read instead. These dates do not represent everything that occurred, just the more significant accusations and trials. Please ask follow up questions since this will not cover everything.
February 1692- Several young girls are diagnosed with afflictions caused by witchcraft: Betty Parris, age 8; Abigail Williams, age 11; Ann Putnam Jr., age 12; and Elizabeth Hubbard, age 18. Betty and Abigail are the daughter and niece respectively of Rev. Samuel Parris and Ann is the daughter of Thomas Putnam, an influential political leader. The girls named Sarah Good, Sarah Osborne, and Tituba as witches. Before you ask, the short answer is we don't know what was actually wrong with the girls. Maybe it was mental health related, but we just don't know. It was not ergot poisoning or anything to do with the rye- https://salemwitchtrialsresearch.wordpress.com/2015/01/04/a-common-misconception-the-ergot-theory-and-the-salem-witch-trials/ March 1- Sarah Good, Sarah Osborne, and Tituba, 3 easy targets for accusations, faced judges John Hathorne and Jonathan Corwin for an examination, essentially a pretrial hearing to determine if the accused can be held in jail for a later trial. Tituba confessed and named Good and Osborne. All 3 were sent to jail.
March 12- Ann Putnam Jr. named Martha Corey, a church member, as one of the witches afflicting her.
March 21- The examination of Martha Corey. A new precedent is set, church members can be accused of witchcraft.
March 24- The examination of Rebecca Nurse. Nurse, a woman known for her piety was sent to jail for witchcraft. If Nurse could be accused, anyone could be under suspicion.
April 11- The examination of Sarah Cloyce and Elizabeth Procter. Cloyce recently tried to petition for the release of her sister Rebecca Nurse. Both women are sent to jail. Elizabeth's husband John Procter, the first man accused of witchcraft, was probably also arrested and examined by this date but the records are lost.
April 19- The examinations of Bridget Bishop, Giles Corey, and Abigail Hobbes. Bishop faced her third accusation of witchcraft in 1692, making her a very easy target. Giles Corey, husband of Martha Corey, was questioned. Hobbes confessed. All 3 were sent to jail.
April 21- Rev. George Burroughs, the former minister of Salem Village, was accused by Ann Putnam Jr. despite his relocation to Wells, Maine years earlier.
April 22- The examination of Mary Easty. Easty also petitioned for the release of her sister Rebecca Nurse. She was released on May 18 and arrested again on May 20.
May 4- George Burroughs was brought back to Salem, now under arrest for witchcraft. His accusers referred to him as the King of Hell.
May 10- Sarah Osborne died in jail.
May 27- The newly appointed governor Sir William Phips established the Court of Oyer and Terminer to hear the witchcraft cases. Lt. Gov. William Stoughton served as Chief Justice. John Hathorne, Jonathan Corwin, Nathaniel Saltonstall, Samuel Sewall, and 4 others served on the court.
May 31- The examination of Martha Carrier. Carrier was from Andover, MA, and sent to jail. She was later referred to as the Queen of Hell. Note- more people were accused in Andover than any other town during the hysteria. Carrier's children were also arrested and confessed, naming their mother as a witch.
June 2- The Court of Oyer and Terminer met for the first time to hear the trial of Bridget Bishop. She was found guilty. Judge Nathaniel Saltonstall quit the court due to the handling of this case. The trial focused on spectral evidence (the visions the afflicted girls had of the accused) and this evidence was the sole reason for her conviction.
June 10- The execution of Bridget Bishop. All those convicted of witchcraft were hanged. There were no witches burned in Salem.
June 29- The trial of Rebecca Nurse. The jury initially found Nurse not guilty, but after further questioning, the judges recommended the jury reconvene. Nurse was found guilty.
July 19- The executions of Rebecca Nurse, Sarah Good, Elizabeth Howe, Susannah Martin, and Sarah Wildes.
Aug 5- The trials of George Burroughs, John Procter, and Elizabeth Procter. All 3 were found guilty. Elizabeth's sentence was delayed due to her pregnancy. Fortunately the trials ended before she gave birth to her son.
Aug 19- The executions of George Burroughs, Martha Carrier, John Procter, John Willard, and George Jacobs Sr.
Sept. 1- The examination of Samuel Wardwell. Wardwell and many others examined during the summer and fall of 1692 confessed, although Wardwell recanted. About a third of those accused gave a confession since it saved them from execution for at least the short term. Had the trials continued longer, it is likely the confessors would have eventually been executed.
Sept 8- The Trial of Martha Corey
Sept 19- Giles Corey died as a result of pressing. He was tortured for standing mute at trial. He refused to plea his acknowledgement of the Court's authority.
Sept 22- The executions of Martha Corey, Samuel Wardwell, Mary Easty, Alice Parker, Ann Pudeator, Wilmot Redd, Mary Parker, and Margaret Scott.
Oct 1692- Sir William Phips halted the trials for spectral evidence to be reconsidered. Rev. Cotton Mather wrote Wonders of the Invisible World to defend the Court's actions. His father Increase Mather wrote Cases of Conscience which criticized the handling of the witchcraft trials. Public opinion clearly turned against the trials.
Jan-May 1693- The Court of Oyer and Terminer resumed but no longer accepted spectral evidence. Those in jail stood trial and were almost all acquitted. Gov. Phips pardoned the 3 women still found guilty. All remaining accused witches in jail were cleared by proclamation.
1697- Judge Samuel Sewall apologized for his role in the trials.
1706- Ann Putnam Jr. apologized for accusing Rebecca Nurse and her role in the trials caused by a deception of Satan.
Source/For further reading: A Storm of Witchcraft by Emerson W. Baker, Salem Possessed by Paul Boyer and Stephen Nissenbaum, The Salem Witch Trials: A Day-by-Day Chronicle of a Community Under Siege by Marilynne K. Roach, In the Devil's Snare by Mary Beth Norton, Records of the Salem Witch Hunt edited by Bernard Rosenthal, salem.lib.virginia.edu