How does Antony stir the crowd in Julius Caesar?

Antony uses his rhetorical skills to stir up the crowd. He is furious that Brutus participated in murdering Caesar, and even more furious that Brutus has just managed to successfully justify the action as a noble service to Rome. The crowd is ready to crown Brutus for delivering them from a tyrant.
Brutus shows his poor judgment in allowing Antony to speak based only on the promise that he not attack the conspirators. Antony takes full advantage of this opportunity to undermine Brutus, completely undeterred by having constraints put on his speech. He simply works around them. A first method he uses is irony: he repeatedly and mockingly echoes Brutus's words about honor by calling Brutus an "honorable" man over and over until the crowd starts to realize Brutus is not honorable at all, but the opposite.
Having begun to sway the crowd of ordinary Romans against Brutus with irony, Antony abruptly turns to sincerity. He moves the crowd by actually bringing out Caesar's multiply stabbed body for them to see and talking to them about how much Caesar loved them and provided for them in his will.
Convinced that Brutus and the conspirators assassinated a man who was their friend and protector for dishonorable reasons, the crowd turns on Brutus.

Marc Antony is not viewed as a threat by most of the conspirators. The only conspirator who wishes him harm is Cassius, but he is dissuaded by Brutus, who argues "Antony is only a limb of Caesar" and "If we cut the head off and then hack at the limbs / Like we were killing in anger with hatred afterwards." As a result, Antony is allowed to speak at Caesar's funeral, under the conditions that the conspirators will speak first and that he may not speak disparagingly about the conspirators while he eulogizes Caesar.
Marc Antony is able to stir the crowd into a murderous frenzy through the use of rhetorical devices such as metonymy, repetition, verbal irony, and rhetorical questions.
Antony begins his speech by asking the Roman people to "lend me your ears...." This is an example of metonymy: a term is used to represent another closely related noun. When Antony asks the people to lend their "ears," he is really asking for them to pay attention.
Antony seemingly complies with the conspirators' request that he not criticize them; he uses verbal irony and repetition. He repeats the line "And Brutus is an honorable man" each time Antony identifies a charitable or otherwise positive characteristic of Caesar's. After the fourth repetition of the line, it is evident that Brutus is not an honorable man and should not be trusted.
Finally, Antony continues with a series of rhetorical questions, such as "Did this in Caesar seem ambitious?" These questions are not meant to be answered literally but serve to excite the crowd and praise Caesar. By the culmination of the eulogy, the crowd is so incensed that they are best characterized as an angry and vengeful mob. This is evident when they encounter Cinna the poet and attack him because they confuse him with Cinna the conspirator just because they share the same name.