Anthropology has a lot to teach us on how people dealt with such large-scale endeavors without the state. If there's conflict, they find a mediator or perhaps hold a meeting between the two groups to hash these things out. Sometimes, two groups would go to war. But anarchy is not merely statelessness, it means a society of consent and collaboration without hierarchy. Previous forms of statelessness may see peoples going to war or exert hierarchy with one another over any sort of disagreement or conflict, but anarchy means means a commitment to figuring out how to settle conflict and disagreements without hierarchy. So yes, anthropology has a lot to teach us on how people dealt with conflict in healthy ways. Sometimes they'd settle conflict in violent ways, but our purpose is to learn from these and do better.
tl;d: how is this done? talk to each other and learn from how people mediated conflict without states.