Anarchism doesn’t wait for a revolution to begin, unlike movements like Marxism-Leninism. Anarchist theory posits that we build the society we want to have in the here and now, by organizing around principles of direct action and mutual aid (see reply from D Quuil below for that). Structures with horizontal power structures like unions, cooperatives, communes and so on. These orgs work by improving the lives of their people immediately, not in some nebulous future, and therefore radicalize those people and attract more (this is why the state and capitalism intensely hates such orgs and work very very hard to suppress and crush them). If those orgs were to go unchecked, their proliferation would destabilize the capitalist system, as those orgs not only do not sustain it as they don’t try to achieve “infinite growth”, nor are led by the profit motive, and most importantly make their members want to resist the aims of the ruling classes (war, slavery, expoitation). This is the process of Prefiguration, for which you can find plenty of info online.

Prefiguration as I mentioned, is inherently destabilizing to Capitalism. In fact, Capitalism itself arrived by prefiguration itself. The liberal classes under monarchy proliferated wage-slavery and exploitation so far and wide, that monarchies that lasted for tends of thousands of years until that point, collapsed in the span of mere hundreds! And surprise surprise, even if a few liberal democracies succumbed to monarchical counter-revolutions, the result was inevitable. Prefiguration works! You can’t stop an idea whose time has come.

Prefiguration works because it has already built the stable societal form which will replace the one that is collapsing. We don’t have to start figuring things out “after the revolution”. This is what I mean when I say that Anarchism doesn’t just pop into existence. Those unions, cooperatives, mutual banks, communes and so on, will continue existing as they were and continue serving the needs of their people. They would just expand uninhibited until the rest of the society is run like them. This is also why we say we can’t accurately predict what a future anarchist society would look like, anymore than a classical liberal under the monarchy of the Bourbons in the 1700s would be able to predict the Industrial Revolution, never mind the Information Age.

So if those horizontal power structures exist and is how the society is run, where is then this “power vaccuum” to exploit? Any would-be capitalist or monarch would have to convince a society which explicitly rejected their ideas, to go backwards into those ideas. Would you willingly give back universal healthcare just to go back to a US-style healthcare system? No, nobody sane does that (even though the full might of the capitalist propaganda would really like you to). Neither would those people want to go back to a much worse system either. People who’ve tasted freedom would rather die than give it back.

I hope this answers your question and if you want to learn more about anarchism, I can’t suggest The Anarchist FAQ enough as a starting point. We even have a weekly book club about it in !anarchism@lemmy.dbzer0.com