Flavius and Murellus are two snooty conspirators against Caesar. In the opening scene, they catch a bunch of commoners celebrating Caesar's victorious return to Rome and try to give them a spanking for not being hard at work. Check out what Flavius says (and pay attention, because these are the very first lines spoken in the play):

Hence! home, you idle creatures get you home:
Is this a holiday? what! know you not,
Being mechanical, you ought not walk
Upon a labouring day without the sign
Of your profession? Speak, what trade art thou? (1.1.1)

• The play opens on a crowded and noisy street in Rome as Julius Caesar returns from battle, where he stomped Pompey's sons into the ground.
• FYI: Pompey is a guy who used to rule Rome with Caesar (they were called "tribunes"). After disagreeing with Caesar about how Rome should be run, Pompey was defeated in battle and assassinated. Just to be sure that Pompey's family and supporters couldn't come after him, Caesar chased Pompey's sons to Spain and defeated them in battle, too.
• Murellus and Flavius, Roman tribunes who are friends of Brutus and Cassius, come upon a group of common people running about the street in their Sunday best when they should be working. The pair asks about the commoners' professions and what they're up to and finds out that they're on the way to celebrate and honor Julius Caesar.
• Murellus and Flavius point out that rather than celebrate this victory, the people should get on their knees and pray against whatever evil will come from Caesar. They imply that Caesar will be tyrannical, having outlived the other two men who should share his power.
• Before parting ways, Murellus and Flavius disperse the crowd and remove the party favors the people have left around Caesar's statue. They hope this will slow Caesar's roll a little bit as he prepares to overthrow the republic and make himself king.

• Caesar, Brutus, their wives, and all sorts of other folks are gathered in a public place. They're ready to celebrate the feast of the Lupercal, an annual party which involves a bunch of Romans dressed in leather loincloths running around the city lashing whoever they find with a goatskin whip. Seriously.
• Caesar's friend Antony will be running in the festival this year, and Caesar tells Antony not to forget to "touch Calphurnia." She is Caesar's wife, and the whip is supposed to cure her "barrenness." (Before we forget, this is the same "Antony" who shows up later in Shakespeare's steamy play Antony and Cleopatra.)
• After broadcasting his wife's business in the street, Caesar hears a soothsayer (a prophet or fortuneteller) call out to him in the crowd. Caesar now hears the famous warning to "beware the Ides of March," but he ignores it.
• Brutus and Cassius meet and talk while everyone else moves on to the next event. Cassius says his good friend Brutus hasn't seemed very friendly recently. Brutus reassures Cassius that "it's not you, it's me," claiming that he's been preoccupied with some thoughts that he'd rather keep to himself.
• Cassius then starts to suggest things that Brutus's own humbleness won't let him acknowledge. Cassius hints that Brutus has a reputation for being a really honorable guy, and that everybody agrees about this except Caesar. As Brutus begins to catch the whiff of treachery in Cassius's talk, Cassius assures Brutus he's being serious about the whole "noble" thing and not just flattering him. Without saying so, Cassius suggests that a lot of respected Romans think it would be really nice if someone like Brutus led Rome, even though it would mean "disposing" of Caesar.
• Their conversation is interrupted by shouts, and Brutus ends by pointing out that he loves Caesar but hopes the Roman people haven't crowned him king. (Remember, they live in a republic, which has no place for monarchs.)
• Brutus adds that he loves honor more than he fears death, which spurs Cassius to continue suggesting they do something to stop Caesar.
• Cassius harps on the fact that Caesar isn't any better than them, so they have no reason to be his subjects.
• In fact, Cassius says, Caesar is a gutless wonder. Cassius tells a story of how Caesar challenged him to a race on the Tiber River, but Caesar got so tired that Cassius had to rescue him from drowning. Cassius describes how Caesar became sick in Spain, had a seizure, and whimpered. Cassius is clearly implying that Caesar is weak and not fit to be a king.
• There's some more shouting that seems to imply that the people are the crowning Caesar, which helps Cassius's cause.
• Cassius drives his point home: Brutus is just as good as Caesar, and they would be cowards if they didn't do something to stop Caesar becoming the "first man" of Rome. Cassius then appeals to Brutus's family history. Apparently one of Brutus's ancestors helped establish the Roman Republic by fighting the tyrant Tarquin. Cassius is basically calling for Brutus to uphold the family name.
• Brutus promises he's not suspicious of Cassius's motives or flattery but asks him to lay off trying to get him to kill Caesar for a little bit. Brutus will think about whatever Cassius has to say, and he gives Cassius hope with the final thought that he'd "rather be a villager" than call himself "a son of Rome" if things continue on the current path (meaning, if Rome ceases to be a republic). Which would be fine, except Brutus has no interest in being a villager.
• When Caesar returns, Brutus notices he and the rest of his crew look pretty unhappy.
• Caesar spots Cassius giving him the stink eye and calls out instructions to Antony: he'd like to be surrounded with fat, happy men, because the "lean and hungry look" of Cassius strikes him as dangerous. Antony assures Caesar that Cassius is noble and not dangerous.
• Caesar continues to say mean things about Cassius: that he doesn't like music, or smiling, or people who are better than him. (Who is this guy, the Grinch?) Obviously, Caesar has figured out that he should not trust Cassius.
• Just then Brutus and Cassius confer with Casca, who has been at the festivities with Caesar. Brutus asks what has put Caesar in such a bad mood.
• Casca tells him that the crowd was gathered to watch Caesar receive a (symbolic) crown. Antony offered Caesar the crown three times, Caesar refused it all three times, and three times the crowd cheered wildly (presumably because of the humility of their fearless leader).
• Casca thinks the crowd was stupid for not noticing how hard it was for Caesar to resist taking the crown. Each time Caesar refused it a little less wholeheartedly. Apparently the whole thing was so upsetting that it prompted one of Caesar's epileptic seizures in the middle of the marketplace. Caesar had fallen down and started foaming at the mouth, unable to speak.
• Even weirder, before Caesar had the seizure, he stood up before the crowd and opened his jacket, offering the crowd his throat to cut. When he came to, he apologized for any weird behavior, blaming it on his sickness, and everyone happily forgave him. Casca is convinced the people would've forgiven him for stabbing their mothers, as they are foolish sheep.
• Brutus asks if Cicero, the great orator, had anything to say about this. Casca says Cicero did speak, but Casca couldn't understand it because he was speaking Greek. (Casca, not an orator himself, doesn't know Greek.) Hence the phrase, "It's all Greek to me." (See, you're smarter every day.)
• Casca also notes that Murellus and Flavius (remember them from Scene 1?) have been punished. They've lost their positions after their little adventure stripping the people's ornaments off of Caesar's statues. Finally, Casca agrees to have dinner at Cassius's place sometime, though he's pretty rude about it.
• After Brutus and Cassius part ways, Cassius thinks he'll convince Brutus to get on the conspiratorial bandwagon eventually, even though the man is noble, or honorable. Cassius is convinced that Caesar treats Brutus with favoritism, making it harder for Brutus to rebel against him. (It's always harder to kill someone who's nice to you.)
• Still, Cassius thinks he'll sway Brutus by faking some letters and throwing them through his window at night. The letters will supposedly be from citizens praising Brutus, and, between the lines, Cassius will suggest that Caesar is too ambitious and should be put down by someone like Brutus. Cassius is certain he can shake Brutus's loyalty to Caesar.

• Cicero runs into Casca on the street that night. Casca's a little shaken up. Though he's seen his fair share of bad nights, he says the sky is dropping hot fire is definitely a first. Casca thinks maybe there's a civil war in heaven, or maybe the gods are raining down fury because the world has displeased them.
• This would all be crazy talk except that Casca's seen worse than bad weather tonight. A slave boy's hand was lit on fire by a torch, and yet it didn't burn. Then there was a surly lion at the Capitol. Also a bunch of women were terrified by a vision they swore they saw of men walking the streets covered in flames. Casca reports the strangest thing of all: a nighttime bird was in the market, during the daytime! Since it doesn't get any crazier than that, it's clear all these things are bad omens. (Seriously, a nighttime bird.)
• Cicero thinks they should hold off on crazy interpretations of the flaming men, lions, and various insomniac birds. He says people basically interpret things to mean whatever they want them to mean.
• After confirming that Caesar will be at the Capitol tomorrow, Cicero leaves.
• Casca then runs into Cassius, who has been presenting himself to the heavens to be struck by lightning. A tad concerned by this behavior, Casca asks Cassius if maybe he should have trembled at the gods' warning instead of going out for a lightning tan.
• Cassius thinks Casca is an idiot. Obviously the heavens are making the world disco-fabulous to signal their serious displeasure with the state of affairs in Rome, where a certain someone, though he is no better than Cassius, has grown too powerful for his own good.
• Casca, dumb as socks, asks whether Cassius is talking about Julius Caesar. A true politician, Cassius does the old "maybe, maybe not."
• Either way, Casca says the Romans are acting like cowards by doing nothing to stop the tyranny, which will only get worse. Casca has heard that tomorrow the senators will crown Caesar king, and that he plans to wear his crown everywhere but Italy.
• Cassius points out where he'll wear his dagger, and basically blabs his plan to murder Caesar.
• The thunder stops (drama!), and Cassius contends that Caesar is only a tyrant because people are stupid and beg to be taken advantage of.
• Cassius pretends to be surprised about revealing so much in front of Casca, who he suggests might like being Caesar's stupid stooge.
• Casca takes the bait and pledges not to tattle. More important, he pledges to join in on the conspiracy to kill Caesar. Conveniently, there's a meeting of all the conspirators starting right now at the old theater, Pompey's Porch. They're waiting for Cassius.
• Cinna, another conspirator, happens to be on his way to that same secret meeting, and they all stop for a chat. Cinna mentions it would be really nice if Brutus was also interested in killing his friend, Caesar.
• To further this goal, Cassius sends Cinna on an errand to plant some letters Cassius has written in various places where Brutus will find them. Cassius has impersonated other Romans in the letters, all of which praise Brutus and suggest that somebody should really off Caesar for Rome's sake.
• Cassius confides to Casca that they'll have Brutus on their side in no time. Casca is glad, as Brutus is well regarded and will make all the nasty things they do seem virtuous and worthy.
• Cassius agrees they really do need Brutus, and by morning they'll have confirmation on whether or not he'll join them.