In William Shakespeare’s Julius Caesar, written in about 1599 and first performed in September of that same year, Shakespeare identifies eight of the more than sixty historical conspirators against Caesar as Marcus Brutus, Cassius, Casca, Trebonius, Ligarius, Decius Brutus, Metellus Cimber, and Cinna. Historically, all of these men were likely involved in the actual assassination of Caesar, except for Trebonius and Cinna.

Trebonius was assigned the task of distracting Mark Antony while the conspirators attacked Caesar.

CASSIUS. Trebonius knows his time; for, look you, Brutus.

He draws Mark Antony out of the way.

Exeunt ANTONY and TREBONIUS. (3.1.29–30)

Cinna is reported to have given a passionate speech in support of the conspirators in the first meeting of the Senate after the assassination, but Shakespeare alters history to put Cinna at the scene of the assassination.

Before the assassination, Cinna tells Casca “you are the first that rears your hand” (3.1.34), and Cinna is the first to speak after Caesar dies.

CINNA. Liberty! Freedom! Tyranny is dead!

Run hence, proclaim, cry it about the streets. (3.1.86–87)

As noted above, Cinna assigns the first attack against Caesar to Casca, and Casca initiates the attack with his line, “Speak, hands, for me!” (3.1.84).

It is somewhat unclear, depending perhaps on the version one reads, if Casca’s line indicates that he’s the first to stab Caesar or if he’s simply one of many “hands” who attack Caesar at the same time, since the stage direction, at least in some versions, directly following Casca’s line is “They stab Caesar.”

The stage directions also indicate that the final blow against Caesar is struck by Brutus, following Caesar’s famous remark, “Et tu, Brute?” (3.1.85).

It’s impossible to know, and Shakespeare gives no clear indication of, the actual order of stabbing blows to Caesar’s body, nor is it possible to know the number and names of the actual assassins.

A physician named Antistius, possibly Caesar's personal physician, examined Caesar’s body after the assassination. Antistius reported that he found twenty-three stab wounds on Caesar's body, only one of which—one of two wounds near the heart—would have proved fatal. Antistius concluded that Caesar’s death would not have been instantaneous, but that Caesar likely died from internal bleeding as a result of that single wound.

Modern interpretations of Antistius’s report and other historical records suggest that, based on the number of stab wounds, the assassination was carried out by five to ten assassins, possibly including those named by Shakespeare in Julius Caesar.

In Shakespeare's Julius Caesar, Cassius, Brutus, and their fellow conspirators are concerned that Caesar will become a king and overthrow the Roman republic. Brutus joins the conspiracy rather late, and only after Cassius plants forged letters in his home, letters supposedly written by members of the Roman populace expressing concerns about Caesar's rise to power. Brutus, thinking Caesar's downfall is the will of the people, agrees to assist in his assassination.

Caesar himself actually rejects the offered kingship three times, but he also ignores the warnings of both the Soothsayer and his own wife. He will not fall to fear, and he will go about his business as usual. So when Decius, a conspirator, arrives to accompany Caesar to the Senate, Caesar goes with him.

At the Senate, the conspirators gather around Caesar, kneeling at his feet supposedly to plead the case of the banished Cimber. Caesar refuses their pleas, for he believes Cimber to have been rightly banished. Then, without further warning, the conspirators encircling Caesar begin to stab him. In some versions, but not all, Casca goes first. Then the other conspirators follow (we are not told in which order). Finally, Brutus stabs Caesar, causing the latter to pronounce his famous line, “Et tu, Brute?” Caesar then falls dead.

The conspirators are quick to cry out “Liberty, freedom, and enfranchisement!” and to declare that “Tyranny is dead!” They then go to work convincing themselves and the Roman citizens that their act of betrayal was just and good.

It's the Ides of March, and Julius Caesar, defying the warnings of his wife and of a soothsayer, has turned up at the Senate house. Not long after walking through the door and engaging in conversation with some of the men about to kill him, he's brutally set upon by them, the conspirators who've been planning his assassination for some time.

One by one, Caesar's assassins plunge their knives into him, certain that in killing the man they believe to be a tyrant and would-be king, they are restoring liberty to the Roman Republic.

We're never told the precise order in which Caesar's murderers stab him; the only information we're given is a stage direction that says "Casca and the other conspirators stab Caesar. Brutus last." Some versions of the play indicate that Casca is the first to stab him.

It's instructive that it should be Brutus, the man who was supposed to be Caesar's closest friend, who stabs him last. This adds to the sense of drama and allows Caesar to express his shock at his friend's betrayal just before he dies:

Et tu, Brute?—Then fall, Caesar. (III, i, 84)

You too, Brutus? Caesar cannot believe that his bosom buddy has participated in his murder. That he's done so, however, is a sign of just how committed he is to the belief that Caesar was a threat to the continuation of the Roman Republic and that, in order to preserve the Republic, it was necessary to have Caesar killed.

In Act III Scene 1, all we have to go by to answer your question is the line “Speak hands for me!” from Casca, followed immediately by the stage direction "They stab Caesar." Simple enough, and hardly detailed. We can only assume that Casca was the initial stabber, his spoken line being an indication that he got the onslaught rolling. And Caesar’s last words—“Et tu, Brutè?—Then fall, Caesar,” do not necessarily indicate that Brutus was last to lend his knife to the cause, but it is generally assumed that he was.  Having Brutus stab last is a very symbolic gesture, Brutus being one of Caesar’s closest friends and confidantes; his betrayal strikes both Caesar and the audience all the more strongly when he comes last in line, and leaves the door open for Brutus's psychological anguish in later scenes.

As for the rest of the conspirators—and there are many—Cassius, Cinna, Trebonius, Decius Brutus, Cimber, Caius Ligarius—there are no specifications as to the order in which they fall upon their leader. And, indeed, it is hardly important, the deed itself being greater than the men who commit it.

Casca is the first to strike, and, after each of the conspirators attack Caesar, Brutus is the last to stab him. The script of the play does not indicate any other order, except that all of the conspirators do stab him at least once.