When I get asked this (or who will fix the sewers, or other questions of this nature) my inclination is say I don't know. When the questions start to get in to talking about guaranteeing things like housing, food, and healthcare, I tend to become more brutally honest. I don't believe that anarchy will alleviate all social inequity. I am not an anarchist because we will all have all the things we need after the revolution. I am an anarchist because I find the world that we live in, one with systemic and violently enforced hierarchies, untenable.
Would I like for everyone in the world to have food and a home and access to appropriate medical care for their needs? Yes. If that was possible, I would be all for it. I just don't believe it is, and don't see much point in spending time spinning out hypothetical frameworks for a world whose contours we can't even begin to fathom. Nor do I believe that there is a one size fits all anarchism that will work for every locale, every particular. Me and the people I surround myself with have needs that are quite likely different from those of you and the people you surround yourself with. Fuck; The people I surround myself with definitely have different needs than I do, so there isn't a universal answer.
This is actually one of the things that I think is hardest about talking anarchy with non-anarchists. Many who might be somewhat sympathetic to a lot of anarchism's tenets want a road map to how anarchy will provide the same or better material quality of life as the Faustian bargain that is living with capitalism, the state, civilization. The sort of anarchy I long for doesn't offer such promises, but it also doesn't come with the trade offs, but that doesn't mean things will just be smooth sailing, most likely far from it.
Given a life without the cushion of state-subsidized medicine, etc., a lot of people will have a pretty terrible time, at least for a while. Elimination of the state and capitalism will fuck up the food chain right properly, and in a way that I probably won't actually survive, given my current skill set and resources. I'm still aiming for that target, not because I want to martyr myself, or see suffering as noble, but because I ultimately detest the condition of the world and would be happier living in a different, as yet unknown one.
I think an interesting way to think about this is to frame it far more personally; How will you guarantee those things for the people you love/feel affinity with? I suspect if we start from the hyper local/personal and move out, we will do much better than if we start from a grand scheme and try to wedge the all the nuanced particulars into our framework, which is, after all, pretty authoritarian.