Though it may sound counterintuitive, the best chance for anarchy may in fact be playing along with the system.
Ask an arbitrary consumer what the first association s/he has with the term 'anarchy' is, and chances are it will be something like 'terrorism', 'car bomb', or 'vandalism'. This is not an accurate association with the anarchist political philosophy, which is merely concerned with the fact that the best government is no government at all (to paraphrase our second president). It is, however, an accurate representation of the political and social tactics of the most media-visible of self-identifying anarchists -- whether or not they agree with the actual concept of anarchy, as many of them are likely to be latching onto a trendy or taboo term the same way satanism has pretty much nothing to do with Satan.
How do we get around this? Anarchy is the only political system that has been described but never implemented, partly because normal power structures have their own defense mechanisms and want to self-propagate whereas anarchy is based on the concept of (to varying degrees of precision) a lack of any real power structure. Anarchy is a hard sell much of the time, especially when every system that is based around the interchange of power is fundamentally anti-anarchy -- a rallying point in terms of realpolitik even between political systems that don't agree upon anything else. Anarchy has traditionally been promoted one of two ways: either by discussing it (the method of Emerson and Spinoza, of whom the former has been totally misrepresented and his message subverted and the latter has been more or less forgotten) or by attempts at forcibly causing it (in the legacy of neo-marxists and other revolutionaries, including those french guys with the guillotines). The former has been unsuccessful because existing power structures can promote themselves far more effectively since to some extent they control many of the major lines of communication, particularly formative public education (which while important can be too easily misused -- we need our kids to read and write, but too many parents go along with the brainwashing and ingrained dogmatism that comes with, even when you cannot reasonably defend it under the label of socialization) and media (albeit indirectly). The latter has largely been a negative, forming the public sentiment that anarchy is a purely destructive force. The more minor forms (poetic terrorism, Operation Mindfuck, situationism, and other general-purpose small-scale benign acts of subversion) have been even less effective on a large scale, despite technologies advancing their effectiveness, primarily because any surrealistic subversive activity (particularly a highly localized one) can itself be easily subverted in the retelling -- and further, the spectacle has its own narrative, often at odds with reality and fighting with it to protect its own integrity by synthesizing into itself any subversive elements. To fight the empire is to be seduced into it.
So, what's a poor anarchist hoard to do?
Well, you can start off by doing what most other fringe political groups do and start a political party. Everyone knows about the green party, the libertarians, the american communist party, and so on -- even if they have never won a federal election and rarely win local ones. The easiest way to spread the idea of anarchy as a workable political system is to create an anarchist party.
But isn't that against anarchy, you may say?
That is precisely it. What better way to break down power structures than by putting anarchists in office? An anarchist party candidate, in my vision, would campaign on the platform that once in office, he will do nothing. He will not show up to meetings. He will not vote on things. He will not sign or veto bills. This would be a negative to any community electing one in the beginning, mind you, but the federal and state bureaucracies are pretty tied up to begin with. As the number grows, the actual legislative and executive branches slowly grate to a halt.