The way I see it, anarchy is essentially small communities getting together to build their own tiny democracies.
I think The Walking Dead graphic novel really shows what anarchy would become. Essentially, everyone would have to have a role in those societies based on their skills and knowledge. Everyone would take care of each other. Decisions would be made through councils with the members of that community where they would debate and vote on key decisions. I think there would still be some form of leadership to steer the community.
People who don't follow the community rules, or act in a manner that is detrimental to the well being of the community would face trial by the community and quickly get expelled. This would be the worst punishment, because you lose access to all the resources, services, and help this community provides.
Correct me if I'm wrong, though. I'm not some scholar on anarchism.