Anarchism would vary depending on what type of anarchist thought is being practiced.
In essence, like chaos theory, anarchism could go anywhere, but at its core anarchism would strive for order, i.e. community, society. At its core is a social network intent on leveling hierarchies, and promoting liberty, equality (symmetry in rights), cooperation, consensus, direct democracy, and justice, not to mention the right to succession. Small units of governance would be the order of the day (or temporarily large ones), with polycentric law, arbitration, restorative justice, and spontaneous order.
Libertarian socialism, not capitalism.
“Fragments of an Anarchist Anthropology” (pdf):
For anarchists who do know something about anthropology, the arguments are all too familiar. A typical exchange goes something like this:
Skeptic: Well, I might take this whole anarchism idea more seriously if you could give me some reason to think it would work. Can you name me a single viable example of a society which has existed without a government?
Anarchist: Sure. There have been thousands. I could name a dozen just off the top of my head: the Bororo, the Baining, the Onondaga, the Wintu, the Ema, the Tallensi, the Vezo… All without violence or hierarchy.
Skeptic: But those are all a bunch of primitives! I’m talking about anarchism in a modern, technological society.
Anarchist: Okay, then. There have been all sorts of successful experiments: experiments with worker’s self-management, like Mondragon; economic projects based on the idea of the gift economy, like Linux; all sorts of political organizations based on consensus and direct democracy…
Skeptic: Sure, sure, but these are small, isolated examples. I‟m talking about whole societies.
Anarchist: Well, it’s not like people haven’t tried. Look at the Paris Commune, the free states in Ukraine and Shinmin, the 1936 revolution in Spain…
Skeptic: Yeah, and look what happened to those guys! They all got killed!
The dice are loaded. You can’t win. Because when the skeptic says “society,” what he really means is “state,” even “nation-state.” Since no one is going to produce an example of an anarchist state—that would be a contradiction in terms—what we‟re really being asked for is an example of a modern nation-state with the government somehow plucked away: a situation in which the government of Canada, to take a random example, has been overthrown, or for some reason abolished itself, and no new one has taken its place but instead all former Canadian citizens begin to organize themselves into libertarian collectives. Obviously this would never be allowed to happen. In the past, whenever it even looked like it might—here, the Paris commune and Spanish civil war are excellent examples—the politicians running pretty much every state in the vicinity have been willing to put their differences on hold until those trying to bring such a situation about had been rounded up and shot.
There is a way out, which is to accept that anarchist forms of organization would not look anything like a state. That they would involve an endless variety of communities, associations, networks, projects, on every conceivable scale, overlapping and intersecting in any way we could imagine, and possibly many that we can’t. Some would be quite local, others global. Perhaps all they would have in common is that none would involve anyone showing up with weapons and telling everyone else to shut up and do what they were told. And that, since anarchists are not actually trying to seize power within any national territory, the process of one system replacing the other will not take the form of some sudden revolutionary cataclysm—the storming of a Bastille, the seizing of a Winter Palace—but will necessarily be gradual, the creation of alternative forms of organization on a world scale, new forms of communication, new, less alienated ways of organizing life, which will, eventually, make currently existing forms of power seem stupid and beside the point. That in turn would mean that there are endless examples of viable anarchism: pretty much any form of organization would count as one, so long as it was not imposed by some higher authority, from a klezmer band to the international postal service.