What did the early Greeks do when they fought?
Originally the Greeks had no laws at all. This was the Greek Pre-legal Period. This worked fine for the Greeks for a time because there were not too many people, each had a substantial amount of land and they didn't bother each other much. When they did bother each other they took care of their legal problems themselves, including killing each other.
As the number of Greeks grew, and the size of Greece didn't, this killing started to create its own problems. The biggest of these was revenge. When someone killed your brother, you would have to kill him, and his brother would have to kill you and so on. This is a period of time when rules started emerging in ancient Greece. This is the Proto-Legal Period. The first rule we know of in this period was to deal with this problem of revenge. That rule was that if you murdered someone you would be exiled (to be exiled is to be kicked out of your town, and never let back in). The Greeks liked this rule, but it didn't do much to deal with the problem of why everyone was killing each other in the first place, so one day maybe a couple of smart Greeks who were having an argument took their problem to someone they thought was wise. This person gave them an objective view of the situation, and his advise. It is important to note that the Greeks didn't have to follow this advice, but generally did, because it was good advice. This started a trend, and most Greeks began to seek this sort of resolution to their arguments.