Well, the answer to this question depends somewhat on the specific strain of anarchism, but for social anarchism, which is the branch I’m most familiar with, the idea is that councils of local people at the scale of the conflict would settle it according to their own internal processes. One successful example of a process from our current society that would be compatible with anarchism is community mediation. But the exact process would in most cases be up to the local community based upon their needs and what works for them.

I think you are right that there is a bit of a tension in terms of governance vs. individual freedom, but this is inherent to all systems of human organization and life. There is a need for governance, but the idea is to make that governance as free from hierarchy and coercion as practically possible. How far one can take this idea is an open question, but I think it’s highly likely that a more liberated society than our current one is very achievable.