How does Caesar die in Julius Caesar?

Apparently you haven't yet read the play. We learn at the very beginning that some members of the Roman senate are becoming fearful and envious of Caesar's growing popularity with the people. They believe he will do away with the republic, and the senate, and declare himself king. Several of the senators, especially Cassius, try to win others to their side. Their prime target is Brutus, who was very close to Caesar (possibly even his illegitimate son). When they eventually do win Brutus over, the conspirators plot to assassinate Caesar. Their plan comes to fruition on March 15, the Ides of March, about which the soothsayer had warned Caesar.

Now, go read the play!

Caesar is assassinated by members of a conspiracy who believed that Caesar was far too ambitious to rule Rome well.  Even his friend, Marcus Brutus, was convinced to join the conspiracy because Brutus valued his country above his friends and family.  Caesar was lured to the Senate House with the idea that the people were going to offer him the crown.  Even though Caesar had previously made a public display of refusing the crown when Marc Antony offered it to him three times, Caesar was still ambitious enough to have accepted absolute power if it had been offered again.  The conspirators stabbed Caesar "three and thirty" times in the Senate House.

Various senators stab Caesar in the Capitol. The play’s opening scene foreshadows Caesar’s controversial standing. The commoners celebrate Caesar’s victory over Pompey, but several tribunes condemn them for being so fickle. Though they now rejoice over his defeat, the plebeians greatly admired Pompey when he was alive. The adulation of Caesar continues at the Feast of the Lupercal, where Marc Antony offers Caesar the crown three times.

Brutus, Cassius, and several other senators worry about Caesar’s growing power. They conspire to assassinate him in the senate. Brutus, who is good friends with Caesar, justifies the murder on the principle that power corrupts. They must preempt Caesar’s power grab to preserve the Republic of Rome:

And therefore think him as a serpent's egg
Which, hatch'd, would, as his kind, grow mischievous,
And kill him in the shell.

Caesar wonders whether he should go to the Capitol on that fateful day. His wife Calpurnia has nightmares about his death, and there are “most horrid sights” in the streets. Several priests sacrifice an animal but cannot find its heart. However, conspirator Decius Brutus convinces Caesar that Calpurnia’s dreams are fortuitous, tempts him with the crown, and suggests he will be mocked if he exhibits weakness.

Caesar calls Calpurnia’s fears “foolish” and goes to the senate. He ignores the warning of a friend and refuses to pardon Metellus Cimber’s brother in an attempt to demonstrate strength. The conspirators kneel to him, but Caesar asserts that he is not changeable like other men but as “constant as the northern star.” The conspirators, including Brutus, stab Caesar until he falls, dying on his famous line, “Et tu, Brute! Then fall, Caesar.”

Describe Caesar's assassination in Julius Caesar.

Caesar was assassinated on the Ides of March by a group of senators led by Brutus and Cassius. 

About a month before the assassination, on the Feast of Lupercal, Julius Caesar was warned by a soothsayer to beware the Ides of March.  He laughed it off, but there was a conspiracy by a group of senators led by Cassius and Brutus.  Cassius convinced Brutus, a prestigious senator, that Caesar was too ambitious and wanted to be king of Rome.  He and the other senators were upset about Caesar’s march on Rome and defeat of the consul Pompey. 

The senators developed a plan.  Caesar’s trusted lieutenant Decius Brutus would make sure Caesar came to the capital. A senator named Trebonius would distract Mark Antony, because the senators worried that he would prevent their attack.  The conspirators would not kill anyone other than Caesar.  Brutus insisted. 

On the big day, Decius Brutus convinces Caesar to ignore his wife Calpurnia’s dream.  She dreamed that he would be in danger, seeing citizens bathing their hands in his blood.  He convinces him that the dream is a good thing and not a bad thing and Caesar goes.  He also tells Caesar the senate is giving him a crown. 

The soothsayer again sees Caesar.  They have a discussion about the Ides of March. 

CAESAR
[To the Soothsayer] The ides of March are come.
Soothsayer
Ay, Caesar; but not gone. (Act 3, Scene 1)

When Caesar gets to the senate, the senators surround him with a suit from Metellus Cinder.  He wants his brother Publius pardoned.  Caesar refuses, saying he never changes his mind.  Casca then stabs Caesar, and the others follow suit.  The last to stab is Brutus.  Caesar is surprised.  He never expected Brutus to betray him.

CAESAR
Et tu, Brute! Then fall, Caesar.
DiesCINNA
Liberty! Freedom! Tyranny is dead!
Run hence, proclaim, cry it about the streets. (Act 3, Scene 1)

Caesar was stabbed 32 times.  The conspirators believe that they have liberated Rome.  They killed Caesar because he was too dangerous, and now that he is gone they feel that the people of Rome will approve of what they have done.  They could not be more wrong.

How is Caesar assassinated in the play?

The assassination of Julius Caesar is one of the most dramatic points of the play.  The scene follows the plot initially hatched by Cassius and carried out by Cassius, Brutus, and the senators: As Caesar stands before the Senate, the senators all take a role in stabbing him.  In this way, they all become equally guilty of his murder and all, through their actions, illustrate their wish to see Caesar dead.

Several people try to dissuade Caesar from heading to the Senate on that fateful day.  His wife, Calpurnia, speaks of dreams she has recently had that feature Caesar's statue, covered in blood.  Likewise, the Soothsayer (a fortune teller of sorts) warns Caesar on two different occasions that he should beware "the Ides of March" -- the 15th of March, which is ultimately the date upon which Caesar is killed. Unfortunately for Caesar, he ignores both pleas and proceeds to the Senate.