Great question! The crowd is one of the most complex characters in the play - and they change throughout the play. First business, of course, is that they demand right at the start that they're going to be the ones calling the shots:
We will be satisfied; let us be satisfied.
Yet their political ideologies seem worryingly changable. First of all they hear from Brutus, who explains that Caesar has been killed because he might prove a tyrant - and the conspiracy was determined to keep Rome a democracy. Caesar had to be killed for the good of Rome.
The crowd are persuaded:
Bring him with triumph home unto his house.
Give him a statue with his ancestors.
Let him be Caesar.
The sharper readers out there will notice that the 'Third Citizen' demonstrates the way that the crowd entirely miss the point of Brutus' speech. If they want Brutus to be 'Caesar' - and Caesar has been killed for being a dictator 'Caesar' - then they clearly aren't politically very switched on.
What makes this scary as well as funny is because, when Antony speaks to them and persuades them that Caesar was murdered, they become very scarily violent and aggressive.
Revenge! About! Seek! Burn! Fire! Kill! Slay!
Let not a traitor live!
Never, never. Come, away, away!
We'll burn his body in the holy place,
And with the brands fire the traitors' houses.
Take up the body.
Go fetch fire.
What's scarier than a violent man? A stupid violent man. And that's just what the crowd are. They go on the rampage without really understanding either point of view. They're very very easily manipulated.
And, I suspect, things haven't really changed today...