Act 1, Scene 1

What happened? Whose fault was it? Who started the fight? Any punishment?

The fight between the Montague family and the Capulet family was so meaningless, petty and frivolous, as whe know that the two families are a great enemies for lots of years. But it is still not right to fight in the streets.
The main thing is the Capulet family who started the fight first. The evidence is that Sampson provoke the Montague's servant first. Sampson said that he will make a rude face at Montague's servants and make them angry, it tells us that it was Sampson who started the fight first and also Sampson's fault.
After that, before anything happens, Balthasar and Abram arrived, Gregory the Capulet's servant, asked Sampson to take out his sword and start to fight.
As whe know that Benvolio wants to make a peace with them, Tybalt the Juliet's cousin does not like the word of "peace", because of Tybalt, Benvolio and Tybalt started to fighting too with each other, more and more people joined to fight
Finally, the Prince stopped them to fight and he said to the Capulet family to come with him and the Montague family come and see him later. I think there is no punishment for them.