The Mayans lived in independent city-states which was being ruled by kings and priests. The spots of the kings were pretty much always given to the oldest son in the family underneath the current father/king of course. Sometimes there were even female rulers. The Mayan's had a code they followed which helped keep order inside their city-states. Some of their rules/laws are pretty similar to what we have today, such as murder, arson, and acts acted against the gods. Since the Mayans didn't have prisons, the crime committers were either killed, turned into slaves, or they had to pay fines.
The Aztecs lived in city-states which were ruled by a monarchy government. In the middle of the city-states, a major city was located. Every one of the major cities the Aztecs lived in were looked over by a leader which was called a tlatoani, which summed up to be the king of that city. The Cihuacoatl was the second in command underneath the tlatoani. The Cihuacoatl's job was to look over the government every day. The capital city of the Aztec government was Tenochtitlan. The Aztecs had pretty much the same laws the Mayans had. Aztecs had courts all the way up to Supreme Courts. There was also one law called the, "one time forgiveness law." This law allowed any person who commit a crime to confess to a priest as long as they haven't been caught nor have they had been caught for any previous crimes.
The Incas lived in in a monarchy ruled by Tawantinsuyu/the government. The ruler of the Incas was called the Sapa Inca. The Sapa Inca had many officers below him such as Viceroy, High Priest, and inspectors. The Viceroy was a very close relative to the Sapa Inca, which goes to figure that the Viceroy is pretty much the Sapa Inca's right hand man. The High Priest right below the Viceroy and the Sapa Inca in terms of power. The inspectors watched over the people to make sure they pay their taxes and everything else a common citizen needs to do. The Sapa Inca created the laws/rules everyone else had to follow. Some harsh results in not abiding the Sapa Inca's laws includes death or even getting your hands cut off if you were caught stealing.