“That’s all very well, some say, and anarchy may be a perfect form of human society, but we don’t want to take a leap in the dark. Tell us therefore in detail how your society will be organised. And there follows a whole series of questions, which are very interesting if we were involved in studying the problems that will impose themselves on the liberated society, but which are useless, or absurd, even ridiculous, if we are expected to provide definitive solutions. What methods will be used to teach children? How will production be organised? Will there still be large cities, or will the population be evenly distributed over the whole surface of the earth? And supposing all the inhabitants of Siberia should want to spend the winter in Nice? And if everyone were to want to eat partridge and drink wine from the Chianti district? And who will do a miner’s job or be a seaman? And who will empty the privies? And will sick people be treated at home or in hospital? And who will establish the railway timetable? And what will be done if an engine-driver has a stomach-ache while the train is moving? … And so on to the point of assuming that we have all the knowledge and experience of the unknown future, and that in the name of anarchy, we should prescribe for future generations at what time they must go to bed … What is important is that a society should be brought into being in which the exploitation and domination of man by man is not possible … “
-Errico Malatesta, Anarchy 
Anarchy is one of the most misunderstood concepts. Which makes sense, since the origins of its prevalence as an idea there has been a concerted attempt by those most threatened by it to malign and slander it. The word anarchy has more or less become synonymous with chaos, violence, disorder & disarray. Which makes sense, from the point of view of the people who benefit most from having an unjust and oppressive society—can’t have people thinking we’re all equals, that’d be quite disruptive to the order of things.
And I’d be lying if I didn’t concede that it’s easy to present anarchy this way. Taken out of context, anarchist actions over the past couple centuries can be presented as inherently violent. Anarchists are not a monolith, there are many who don’t believe in violent actions and that’s not an invalid position to hold (though it is one that I disagree with personally for a variety of reasons, not least of which being that Nonviolence Protects the State). The thing about violent actions committed by anarchists is that generally speaking they are carried out in an attempt to prevent further, and often greater, violence. Beyond that, there’s a misunderstanding about what violence actually is, for example actions such as property destruction are often mischaracterized as violent by capitalists and propertarians.
“…so our struggle is a constant tension where what we must destroy and transcend is much more obvious than where we might end up.”
-Dark Matter Publications, Beyond the “Movement” – Anarchy! 
Anarchy is a method of organizing, and nothing more. It’s a way of doing things that necessitates and demands that not one person is better, more important, more valuable, more deserving than any other people. I’ve always been very struck by the quote above from Dark Matter Publications. Few things I’ve heard have ever felt more true.
Regardless of whether we know where we are heading or not, there’s no reason to believe that the people of the world would commit acts of violence and create chaos just because the state, which functions by threatening and enacting violence, are removed from our lives. Beyond that, I think the absurdity that follows from a line of questioning, as exampled in the Malatesta quote, ought to be considered. Most people can’t answer those questions about the current society, but they trust that these things are dealt with by those who are concerned about them. If we consider education in an anarchist society: what would that look like, how would it function? Isn’t it reasonable to figure that the people who are interested in making it happen would come together and work out a system? Is that not essentially how it functions currently?
As an anarchist, I can confidently tell you what systems need to end, what practices need to be destroyed, but not what will happen when the days of destruction are behind us.While anarchism is not inherently violent, it must be noted that the destruction of the current unjust system will necessarily be violent. This means that there ought to be a broad support for a diversity of tactics, which will likely include violent actions. Whether or not the supporters of these actions are prepared, capable, or willing to engage in violence themselves is not relevant. Violence, being something very difficult to engage in, is not expected from everyone, as it would be unreasonable to demand that everyone who wants for a revolution to act with violence or take part in violent actions. It is however incumbent on all who want for change, to embrace the fact that violence is often what makes change to occur. And after the revolution, what we will need is constant revolution and constant change, because anarchy is not static, and it is not a (violent) state of being—it is a way of doing things, an active method, it is fluid and ongoing.