As long as it takes until people learn how to look after themselves.
You hit the nail on the head. Those unwilling or incapable of looking after themselves will never embrace or even understand Anarchism because they basically see the state as their meal ticket.
To paraphrase Upton Sinclair, it is difficult to get a man to understand something when his survival depends upon his not understanding it. That's why hardcore statists are constantly pushing food stamps, obama phones, and other free goodies. They want you dependent.
How to bring about Anarchism? First, you need to get yourself self sufficient. Once you achieve self sufficiency in the areas of food, shelter, transportation and defence, help others do the same. Share information and ideas, things like Bitcoin for example. If enough people do that, my hope is that the state will gradually and naturally begin to fade away. The main idea is to get people self sufficient and off of food stamps.
But in my experience, the best way to turn around a liberal is to take them to a shooting range. Not only is learning self defence fun, but it plants a seed of doubt in their mind and naturally gets them to question necessity of the state.
That's how I see it being done: winning over hearts and minds, one person at a time.
I disagree that the unwilling and incapable see the state as their meal ticket. The majority of nations in the world have no or very limited welfare systems.
On the other hand the majority of nations in the world support the economic elite and keep the divide between rich and poor as large as possible. The "elite" certainly see the state as their meal ticket.
I would hope that hearts and minds would work but as long as anarchists are branded as mask wearing extremists trying to undermine "the system" then one person in a life time might be a realistic goal.
If you want anarchy, take away the rich nations', tv, newspaper, internet once you've removed the media you´ll remove apathy and the poor will wake up to how shit their lives really are and start doing something about it.
There is also the problem that WE anarchists have a tendency to distance ourselves with the political process as it serves a system that we don't agree with. A few more of us need to exploit the system and participate in what THEY call democracy and try to instigate change from within.