Act 3 scene one, explain how the events in this scene are simlar to the events in Act 1 scene 1

The above answers are correct in citing the main similarity between these two scenes is the fact that these are the two main scenes of physical fighting between the Capulets and the Montagues.

What makes these two scenes most parallel, in my opinion, is the way each fight starts.  Though the fight in Act 1 is begun by two servants, it starts with the exchange of petty insults.  The fight grows larger because members of each house, without thinking about the reason behind the conflict, join the fight to stand up for their respective families.

The fight scene in Act 3 is very much the same, except that this time, though Tybalt believes he is being insulted by Romeo's kindness, Romeo's intentions (for once) are pure.  Tybalt does not even recognize this because he has grown so accustomed to automatic scorn and hatred (both for and from) the Montagues that there is no reason for him to consider Romeo to be genuinely kind.

It was necessary for Shakespeare to include the first fight scene to set the tone for the second and to show the sort of hidden seriousness of the hatred between the families.  Both are started because one house feels insulted by the other.  Neither of the fights are justified which heightens the pettiness of the overall feud between these families.  Additionally, there is a bandwagon effect in both fights, which displays the sense of automatic (if irrational) loyalty by the characters to their respective sides.  Consider that Mercutio, who isn't even related to the Montagues, fights as if he is Romeo's brother.  Then, only when he is mortally wounded does he realize just how out of hand the hatred has become.  His famous line, "A plague on both your houses!" is the alarm that, at last, it has gone too far.

Though a dramatic comparison, it should be noted that entire wars have started as a result of one leader feeling insulted by someone.  Gang violence and warfare so prevalent in major US cities could likely be traced back to a series of once petty insults that escalated to full blown hatred.  In just two scenes, Shakespeare has captured several common human emotions, desires, and actions that result from what is often passed off as "petty insults."