It's based on property rights and the non aggression principle.
In other words: bigger guns
Basically as it is now but instead of the law and tax being collected based on location, you get to freely choose what law(s)-enforcement you want to be under.
Until someone under a different LE company accuses of a crime. Then you'll be subject to their process (unless, of course, your LE company has more guns).
why would you ever agree then? Well maybe because they have an agreement with your LE company and you'd find yourself dropped as a client if you didn't or you both use the same insurance company and they'd jack up your rates if you didn't. More extremely you might be fired and become unhireable as a liability and unless you already have sufficient arable land to subsistence farm you will die of starvation or be shot for trespassing (initiating force) on the sidewalk that you can no longer pay for the use of.
Don't take this as me thinking it is at all a workable scheme also I'm definitely not AnCap and I don't hang out in their circles so this kinda just the low-nuance version that I've picked up via osmosis.
The last arguments of kings are still guns.
The end state of all theoretical non-aggressive libertarian societies is that they are conquered through force by some form of cartel. In my opinion, seasteading, which is predicated on mutual non-aggression for prosperity, is strictly inferior to hiring a bunch of ex-CIA and ex-GRU contractors to destabilize and take over a pre-existing dictatorial country, and then rewrite its laws from scratch. The moral high ground loses to boots on the ground, every time.
If you can't or won't preemptively attack and annex another country's territory, you're better off trying to colonize space, where nation-states can't reach you as easily, or start by building the nuclear warheads, and then build the floating cities. The veneer of civilization is thin, and one gun is no longer sufficient for one man to defend his castle.
Obligatory Blockchain woo preemption:
"The agent's model of what you are interested in would always be a cartoon, and in return you will see a cartoon version of the world through the agents eyes" - Jaron Lanier
Anarchism was overwhelmingly a socialist movement, contemporary with Marxism and communism. Many anarchists debated the ideal forms of socialism vigorously at congresses held by groups like the First International. Historically, Marxism and communism won the most mindshare, with rare exceptions like the Spanish Civil War.
Leading 19th c. anarchist thinkers, like Bakunin and Kropotkin, would have laughed you out of the room if you had claimed anarchism was in any way not a leftist movement.
This conception is from a much later argument of economist Murray Rothbard from the mid-20th c., and owes more to the Austrian school of economics then any strain of anarchist thinking. Rothbard drew upon some individualist anarchist writers, but tossed out all the economic parts he disagreed with, and called it anarcho-capitalism. Claiming anarcho-capitalism as a form of anarchism reveals a complete misreading of, or disdain for, the overwhelming majority of anarchist thought.
Now for an interesting follow-up: the term "libertarian" underwent the same change in America, but even more thoroughly, to the point that only historians recall its leftist origins. (Outside America, "libertarian" is more synonymous with anarchism.)
To quote Rothbard above: "One gratifying aspect of our rise to some prominence is that, for the first time in my memory, we, 'our side,' had captured a crucial word from the enemy... 'Libertarians'... had long been simply a polite word for left-wing anarchists, that is for anti-private property anarchists, either of the communist or syndicalist variety. But now we had taken it over..."
Anarcho-capitalism is not a type of the former, but it is a type of the later.
https://www.reddit.com/r/Anarcho_Capitalism/comments/3ucp8y/...
The whole debate feels like a fruitless exercise to reclaim territory that is long lost.
I'd call myself an "anarcho-pragmatist" now. That's based on not wasting breath or effort on stuff that's almost guaranteed not to work. My current recommendations to like-minded individuals are to support labor unions (or invent some other institution that counters plutocratic trends), and to oppose consolidation of broadcast media. I have long ago abandoned the non-aggression principle as being too dependent on people arguing over the meaning of "aggression".
Anarcho-communism is contrasted by anarcho-syndicalism, which argued for unions/industries being the organizing principle rather than communes/towns.
relevant subreddit: