In my personal opinion the best thing to do is to bypass the stage of an "Anarchist State" which I see as a complete paradox and not consistent with Anarchist beliefs.

Build the movement to the stage where we can set up anarchically organized systems that do the jobs of Capitalist and State systems. At which point those Capitalist and State systems can be dismantled safely.

The problem is that the state will attempt to preserve itself to varying degrees depending on the Authoritarianism of the regime.

So there's two options.

In the case of a progressive, freethinking society which doesn't silence dissenters, think Scandinavian countries with strong workers movements. Though they aren't at this stage yet, they are closest we've got right now. The Pirate Party being a good example of progress towards this.

There you can work to peacefully transition to an Anarchist system through simple spread of information. Provide enough evidence for your conclusion that Anarchism is the best way forward to enough people, and take the steps to establish autonomy from the state and capitalist systems. When you starve those systems of people to work in them, they will naturally collapse. If they don't, well you've just successfully created a decentralized self sustaining system of your own to live within.

In an Authoritarian Police-State it's probably time to start thinking of a violent revolution.