My impression from talking to and reading stuff by anarchists is that the idea is for culture to serve in the place of sticks and rules. As for the mechanics of how this works, what such a culture would need to achieve to succeed and how it could do so, frankly most of them seem to take it on faith that this will be the easy part and naturally fall into place as soon as their oppressors are no longer mucking things up.

Which is a shame because I think it could be totally plausible and worth seeking, if you worked through the game theory and sustainability-over-time issues, despite being a monumental challenge and being about something as crudely understood as collective psychology. Human society is a system, and systems can be designed lots of different ways. It could be possible to have a culture that is powerful or clever enough to allow for a large population to function without a controlling state beating people into line.

Not directly related to this comment but I also want to mention and recommend the book The Disposessed by Ursula K. Le Guin, really thoughtful novel about anarchism.