When the government of the nation fell apart, the Nephites easily divided into tribes. The reason that they so easily fell into tribal organizations is probably because those divisions had never completely left the society. We hear of people of different tribes throughout the text, and they were probably representative of a principle of organization that operated on a more local level. Therefore, the collapse of the government that unified the tribes did not create anarchy, but simply removed a unifying layer of government.
Within the tribes, there had already been an organizational structure. Even if the person who eventually became the “chief or leader” over them had already been the figurative head of the tribe, there was probably a “voice of the people” to sustain them in the more direct ruling role.
Tribal rule did not mean that they were small, as indicated in verse 4, which states that “their tribes became exceedingly great.” As an organizational unit, the tribe held together smaller units, which might (in more modern terms) be called clans, and then families within the clans.