old post but reposting a comment:

it ends up looking a little bit like government but not the same

consider if there was no government: people might be able to shoot each other, but if person A shoots person B, then person B's friends might shoot person A, so they end up coming to an agreement of not shooting each other (a law, voluntarily agreed to: "on my property you will not shoot me or I will shoot you", something like that), these kinds of agreements will be made with respect to trespassing or stealing or whatever else.

These kinds of laws might become standardized and multiple properties would accept them so that in effect stealing or trespassing might be illegal everywhere.

You might ask, "but what if someone just wants to break the law anyway?" Well, that's the same as under a government, some of the same threats of consequences exist if people break laws, it's just different who enforces them.

Now you could set up courts and people would make use of them because, just like under the State, if people will not make use of the courts then they are in "contempt of court" and subject to whatever penalties.

Say person A shoots person B and now person B's friends want to have a trial about it, but they won't go to court. They are subject then to person B's friends shooting them at the extreme, or less extreme subject to lesser penalties person B's people might attempt.

This is all kind of a thought experiment, but to me it seems pretty easy to see how anarchy matures into something that looks like government but there's not just one government entity in charge of everything. (Just like thinking about if you were to build businesses from scratch, about how that would be developed)

Also you might want to read about "no rule of law" situations, or what happened in countries where the rule of law broke down like when there were civil wars. Ancap would build further beyond those primitive conditions but it shows what the starting point is. (Some of them might not be the best examples but rather would be more like states)

To me I just envision everything we have now but it's owned by private entities and instead of there being like one roads company for example, there might be multiple road construction agencies.