a. there are many ways, plenty you probably learned of even in state-sponsored school... feudalism and tribal cultures are commonly known about, just off the top of my head.
and for how to organize stuff and its flows, gift exchange and barter are both dramatically different from capitalism...
history and anthropology are both fields that are biased, but give us clues about other ways we have lived. some science fiction or speculative fiction gives us ideas too.
b. some anarchists are not interested in organizing society, and see it as an inherently alienated way to think about living with people. (the idea of thinking on those terms, of believing in, expecting and/or wanting to, manage how people live with each other, that's all part of the problem we want to get away from.)
ps: please tag your questions.
My own hardline misrerabilist answer to this question is that perhaps there is no other way of organizing society. Not in the sense that there have never been other styles that would have been preferable, but more simply in the sense that by now fundamental things about the world have changed so drastically that such arrangements may no longer be possible. That is, the world population vastly exceeds the world's carrying capacity; very many species + natural systems have been obliterated or damaged, and more will follow very shortly; there's not any longer an unenclosed wild space. It's perhaps to the point that human survival is inextricably dependent on massive technological systems beyond our control. Such systems can only be administered by capitalism + the state, really. True we don't live well by continuing this way, but I wonder if we have a choice. I wonder also about what further damage we do to ourselves by imagining that we might. This I suppose is what Margaret Thatcher had in mind when she informed us that "There is no alternative."Although this is more related to the second part of dot's answer than the first, I don't see it as being in tension with dot's answer at all. My perspective is of course that, as dot has said, envisioning a total social organization (whether this is possible or no) would be a bad idea. I'm going to quote for you from an interview Foucault gave, called "Revolutionary Action: Until Now":
“I believe… that this particular idea of the ‘whole of society’ derives from a utopian context. This idea arose in the western world within the highly individualized historical development that culminates in capitalism. To speak of the ‘whole of society’ apart from the only form it has ever taken is to transform our past into a dream. We readily believe that the least we can expect of experiences, actions and strategies is that they take into account the ‘whole of society’... But I believe that is asking a great deal, that it means imposing impossible conditions on our actions b/c this notion functions in a manner that prohibits the actualization, success, and perpetuation of these projects. The ‘whole of society’ is precisely that which should not be considered except as something to be destroyed. And then, we can only hope that it will never exist again.”
(You can find the rest of this in Language, Counter-memory, Practice and maybe online as well.)
Maybe this is not what you meant to ask. I don't know. Anyway I hope it's interesting.