The term "anarchy" is derived from the Greek "anarchos" ("without ruler").
Up until the 19th Century, the term was ordinarily used in a positive manner (by Proudhon in his 1840 work What is Property?), to describe a intelligible political belief, and it was only later that it became used to signify something affiliated with chaos. If you ask any modern day anarchist that was purposefully done to smear campaign an idea that will be powerful for the people.
Anarchism may be defined by the dictionary as: opposed to the government in all its forms. But it would be wrong to think of anarchism as essentially negative. The opposition to the government comes from a belief about a society which is positive.
What does it mean to be an 'anarchist'?
It means to be self-governing and take full responsibility for your own life.
Anarchists are frequently associated with Molotov cocktail throwing and destruction in the streets, but anarchists have actually sought a more ordered and ethical society.
All of the anarchists I know reject the idea of an involuntary hierarchy because that is equal to slavery.
To support an involuntary hierarchy is to support slavery. If governing yourself is not at least an option in society, it's hard to argue that society is made up of anything but forced and coerced modern day slaves.
Some say anarchists reject all hierarchies (and some apparently do - anti-landlord anarchists do exist!), however, once questioned all that I have met will agree that humans can enter into a voluntary hierarchy - like say an employer/employee relationship - as long as it is voluntary, it is ethical.
Violence, contrary to popular belief, is not part of the anarchist philosophy. Initiating violence at least. Defending yourself from violence should not be confused with initiating it.
That being said, I have had open discussions with anarchists who view what the state or police are doing is a violation of their personal liberties and life and won't hesitate to defend that with force.
Of course, there is also a handful of anarchists that think that the only way to prevent further, what I like to call, 'fuckery' perpetrated by the state - is by taking out the system with brutal force (after all it would be in self-defense, right?)
It has been pointed out by most anarchist thinkers that the revolution cannot be won, nor can the anarchist/voluntaryist society be established and maintained, by armed violence.
Philosophical Anarchism is the view that the State lacks moral legitimacy, that there is no individual obligation or duty to obey the State, and that the State has no right to command individuals.
Anarchists mostly disagree over the means to be utilized to achieve their end game, varying from extreme violence to non-participation and taking in all points in between – anything, that is, other than "legal", "state" or "constitutional" action.
Speaking from personal first-hand knowledge, many self-proclaimed "anarchist" I have personally met actively practice the NAP or Non-Aggression Principle.
The non-aggression principle is an ethical stance which asserts that "aggression" is inherently illegitimate.
Can you imagine a "state" that doesn't use aggression?
The FREE MARKET
The Free Market: advocates an economic system based on voluntary market interactions without the involvement of the state. That means NO STATE INVOLVEMENT WHATSOEVER. The closest thing to this nowadays is the black market but even that is influenced and affected by state involvement.
A strategy as an anarchist for improving society is to influence public opinion.
Natural anarchists: people who, while not identifying themselves as anarchists, think and behave in significantly anarchist ways.
In the long run, rulers need the consent of the ruled. No government, however authoritarian, can keep going if it gets too far out of touch with public attitudes. If enough ordinary people are determined on some specific relief of government, then the government must either surrender or fall apart.