According to benvolio who started the fight

This is what Benvolio says (talking to Montague).

"Here were the servants of your adversary,
And yours, close fighting ere I did approach:
I drew to part them: in the instant came
The fiery Tybalt, with his sword prepared,
Which, as he breathed defiance to my ears,
He swung about his head and cut the winds,
Who nothing hurt withal hiss'd him in scorn:
While we were interchanging thrusts and blows,
Came more and more and fought on part and part,
Till the prince came, who parted either part".

What actually happened was that Sampson and Gregory (Capulet servants) intended to provoke some of Montague's men into a fight. With Sampson biting his thumb, a verbal argument soon escalates into a fight between the parties. Benvolio then comes along sees the fight and tries to stop it by beating down their swords, using his own to do so. Tybalt then comes along and seeing Benvolio with a drawn sword, attacks. The fight then escalates further with the general citizenry joining in.

Therefore doing a quick precis of Benvolio's words - I saw your servants and those of your adversary (Capulet) fighting. I drew my sword to try and stop them. At that very moment, Tybalt appeared and seeing my drawn sword attacked. I asked him to cease, but he defied this request and wouldn't stop, expessing scorn for Montagues. We were skirmishing, and then more and more of the general citizens joined in, escalating a small disturbance into a major melee until the prince stepped in and stopped it..