There is many misunderstandings of an anarchist society. Anarchy simply means figuring out how to work together to meet our individual needs, working with each other rather than "for" each other; and when this is impossible, it menas preferring strife to submission and domination.
It means not valuing any system or ideology above the people it purorts to serve, not valuing anything theoretical above the real things in this world. It means being faithful to human being (and animals, and ecosystems), fighting for ourselves and besde each other, not out of "responsibility," not for "causes" or other intangible concepts. It means denying that there is any universal standard of truth, aesthetics, or morlaity, and contesting wherever it appears the doctrine that life is essentially one-dimensional. It means not forcing your desires and experiences into a hierarchical order, but acknowledging and embracing all of them, accepting yourself. It means not trying to compel the self to abide by any external laws, not trying to restrict your emtions to the sensible or the practical or the "political," not pushing your instincts and passions into boxes: for there is no cage large enough to accommodate the human soul in all its flights, all its heights and depths. It means seeking a way of life which gives free play to all your conflicting inclinations in the process of conti nously challenging and transforming them.
It means refusing to put the responsibility for your life in anyone else's hands, whether that be parents, lovers, employers, or society itself. It means taking the pursuit of meaning and joy in your life upon your own shoulders.
There are many different ideas of how an anarchist society should be formed based on economics. Generally however, the belief in mutual aid as opposed to competition exists. Mutual Aid means people working together to accomplish things, as opposed to working against each other in the current way. Capitalism puts us against each other, we are constantly at odds and at war with each other to get to the top. Anarchy is the recognition that society is better served working together, and we all benefit more from mutual aid then we do the current way of things. A society without hierarchy is what it represents, where no person is above another. We seek to eliminate hierarchy in all forms whether it be economic (capitalism, wage-slavery, state socialism, ecological degradation), political (nation-states), or social (sexism, racism, homophobia, etc). It is a society based upon complete and widespread direct control by all people over their needs and existence. This means a totally self-organized and self-managed society with power generating from the bottom and spread out horizontally to others. This means people freely, ecologically, and autonomously working together for our own needs and desires, not for profits or for the state.
Those with little understanding of the past tend to propose that this society is impossible to have. The version of society which anarchy seeks to create though, has been seen before, and even exists today. Similar ideas have been expressed by other groups and peoples such as the Situationsits, autonomists, and more. We can see these types of self-organized communally run societies existing in the lives of those who are still living a gatherer-hunter way of life such as the !Kung of the Kalahari desert, the Hadzabe of Tanzania, the Mbuti, and others.  Hierarchy developed only about 10,000 years ago with the creation of agricultural societies as opposed to hunter gatherer societies. Societies without hierarchy existed for over two million years, they were egalitarian and based upon equality. There was no surplus in this nomadic way of life and no domestication which meant no class, and no war. Humyns lived this way of life for over 99% of our existence.
Hierarchy in one form or another is the reason why there is war, and to back this up with archaelogical reference, there is no evidence to suggest war before domestication started, and we can see today that only within groups that have domesticated plants or animals and shown their domination over them that there is war.
Anarchy represents a world with ultimate freedom and equality for all, for our hearts should desire nothing less as human beings. Many would like to think that America is a free nation without putting serious thought into it. The American government has made it so we are not free. When meaning is already attributed to every action that we could possibly have, we are not free to act. Within America there are laws which are in place to protect the rich, their profits, and private property in order to help keep the status quo the way it is, therefore, every individual who follows the laws is supporting her own slavery. As one anarchist once said, "laws are cobwebs for the rich, and chains of steel for the poor."
Obviously then, an anarchist society would not have police. Many feel the police are there to protect us, but the purpose of the police is only to enforce the laws, and thus to enforce the status quo. We have been indoctrinated to believe that there are criminals in this world and there are good people, but it is the inequality of the world capitalist system which causes the breakdown of social order which causes the inequality which causes people to act in ways which are "criminal". Besides, in the current system, crime is an arbritrary thing and we are seeing the system enforce thought crimes more than things determined by law. Who is to say that their laws are just in the first place though? We are convinced that we need to follow them, yet, they benefit us in no way. An anarchist society would create equality for all which would make crime obsolete. Crime is also the result of insanity. The current systems solution to all of this is to put a person in a prison (what about this seems right to anyone), and lock them up until the State decides they can leave. Radical mental health meetings can be had instead with a community based support for a person helping to develop mental health and to help them with their problems, while not judging and showing understanding. Throwing someone in jail for not being mentally healthy is a sickening act which is wrong in all of ways. Many will ask what if someone murders their wife, what will happen? I will not go into such narrowly confined policy questions and get into "politics". It is my belief that the current organizing of society is what creates all of this bullshit which exists. The stress and pressure one endures at work, could force him to become angry in life and to harm his wife, or maybe he will beat his wife based off the fact that they have grown apart and this society wants to make everything permanent and infinite, which often can create many problems. Anarchy is the abolition of all laws, rules ,and restrictions, as well as all classes. Anarchy is also the abolition of the monetary system and the wage system, in order to create a society which is based off of a gift economy, not capitalism.
Anarchists tactics include direct action which is bypassing authorities to accomplish things ourselves. Direct Action in most forms is illegal, but if it was legal, it wouldn't be very effective. Direct Action is a way to handle the problem directly. This means, not relying on representatives in Congress who have been bought off by corporations to do things for us, but taking things into our own hands. When it comes to politics, this can be mean workplace occupations, ecosabotage, squatting, demonstrations that take place without permits or permission, etc. In everyday life it can be seen as dumpster diving, theft, and even growing your own garden to get your own food as opposed to buying it indirectly. Violence is as much a strategy and tactic within direct action as non-violence is. There is no "anarchist" way aside from direct action and decentralized approaches to activism. The revolution cannot be accomplished by asking authorities, or hoping they will concede, it can only be taken. Direct Action then liberates the person and focuses on the realization that there is no authority but yourself. As far as violence as a tactic goes, many are against it as if it is instigated by anarchists. In reality, the violence is only in response to State and Corporate violence against the environment, human beings, animals, and others. Violence as far as eco-sabotage is a recognition that the only thing that the corporations care about in this society is money and how much something effects their bottom line. One can go and protest in front of a bussiness which is destroying the environment or they can do multiple things including destroying the machines which are being used to destroy the environment, or a person could treesit to ensure that they cannot cut down the treets, or they could spike the trees and warn the forrest service, thus preventing the cutting down of the trees. Violence as in the form of self-defense against police attacking the people, can never be ruled out of course for it is truly defending our lives. Police have murdered people before for their activism (see: Carlos Giuliani), and they have beaten people bloody for their activism, and anyone who will stand back and allow their comrade to be beaten by police clearly has no concern for them and shouldn't be involved in that sort of activism.
In the current system, we are forced into violent relationships. Our whole lives surround our work and making money as our self-worth becomes determined by the amount of money we make and the decency of our job. Work however, is the most oppressive miserable thing there is. It is a dehumanizing experience which strips us of life and creates us further into obedient slaves. Work discourages individuality and seeks to keep us in line. It was once put outside a Nazi concentration camp, "arbeit marcht frei", meaning "work makes one free", something which should automatically create a disdain for work. With work, we slowly work away our lives in an attempt to be able to attain money to buy the products which were made with our own labor so the people at the top can become richer, as we struggle to get ahead. In an anarchist society, work will be abolished. Many will assume this means that nothing will get done, but it is not that nothing will get done, merely that things will be done in a different way than they currently are, a way that is enjoyable, and when we "work", we will be "working" with each other to achieve our individual needs as opposed to working against each other to get ahead. Work also will not be something dictated, and there should be no time schedule enforced, no 9-5 workweek, or anything imposed upon a person, for everything in an anarchist society is voluntary, and there is no force.
The last statement will make people question how anything will be done. Why wouldn't things get done though? When we are working together for our own needs, when we are working not for the State, for the economy, for the employer, but for ourselves, why would we not want to do things for ourselves? This is a question which shows no logic realy, and presents people as being so stupid that they would rather die than have to work. If this was so, then no one would work today. In a sense we are forced to work, yes, but in a sense every person can choose not too as well. Every person can do absolutely nothing for their survival if they want and they can die. Yet they don't in this system, so why would they in a society that benefits them? Many want to presume that they are good enough to allow this society to work, but the fault lies within everyone else, but this shouldn't be of concern, for every person is good by nature, it is a matter of the external circumstances which exist in todays world which force them to act in a way that is seen as wrong. In an anarchist society, each individual needs to be concerned with themselves, for we are to be responsible for ourselves and no one else. The indoctrination which we experience all throughout life trains us to behave in ways which are not beneficial to society, nor to ourselves. It is this indoctrination which forces people to cheat on their wives because we are so centered on only one of everything, it is this indoctrination which has people killing their loved ones because they have cheated on them, or because we feel they are cheating on someone. We never learn to share in this society, and we are taught to view everything in terms of ownership. Ownership is as arbritrary of a thing as the concept of nations, neither is real, and both are only imaginary.
How can this society exist with so many different cultures and differing people? Because anarchy doesn't require obedience, and it doesn't require conformity. Individuality is a product of anarchy, having people think for themselves and become their own people. It is also a matter of having people recognize themselves as their own authority and recognizing for themselves what is best for them. An anarchist society is in the end, what the people make of it. There is green anarchy, anarcho-primitivism, anarcho-communism, and many other anarchists beliefs of how society should be organized, it is a matter of the people themselves organizing society in such a way that they are in control, that everyone has freedom, and no one person is above another. In this world, each person will have the freedom that a president has, and she will be able to determine things for herself, as opposed to someone else determining things.