How did Cassius persuade Brutus against Julius Caesar?

Although Cassius sensed that he was bringing Brutus around to joining his proposed conspiracy, he decided to follow up by sending him counterfeit letters purportedly from various important Roman citizens urging him to act against the tyrant Julius Caesar. Shakespeare got this, as he did so much of the information used in his play, from Plutarch. The playwright has Cassius say to himself at the end of Act I, Scene 2:

I will this night,
In several hands, in at his windows throw,
As if they came from several citizens,
Writings, all tending to the great opinion
That Rome holds of his name, wherein obscurely
Caesar's ambition shall be glanced at.
And after this let Caesar seat him sure;
For we will shake him, or worse days endure.

In Act II, Scene 1, we see how Cassius's ploy has an effect on Brutus when he reads one of the phony letters.

He opens the letter and reads.
"Brutus, thou sleep'st. Awake, and see thyself.
Shall Rome, et cetera? Speak, strike, redress."

And to show that this is only one of many, Shakespeare has Brutus say to himself:

Such instigations have been often dropped
Where I have took them up.

Cassius must have Brutus on his side if his plot is to succeed. By himself Cassius does not have the charisma to attract co-conspirators. He is a selfish, miserly man with a reputation for having a bad temper, using threats and abuse to get his own way. Anyone who knows him would regard his proposal to murder Julius Caesar as being motivated by his own selfish interests. Caesar dislikes and fears Cassius. If Caesar became absolute ruler, he might have Cassius liquidated. And Cassius knows it! He is desperate, and he is operating under severe time pressure. A good illustration of his selfish character is to be seen right after his meeting with Brutus in Act I, Scene 2.

Caesar doth bear me hard, but he loves Brutus.
If I were Brutus now and he were Cassius,
He should not humor me.

Cassius would have no objection to Caesar being made king if it would do him personally any good. He and Brutus become partners, but they are entirely different types of men. Brutus is patriotic and altruistic, whereas Cassius is totally selfish and greedy. They were bound to have conflicts sooner or later. Their final conflict erupts in the quarrel in Brutus' tent in Act IV, Scene 2, just before the battle at Philippi.