Basically it would mirror Communal living that you see in areas like here or here. With the exception that these communities are forced to live within the legal structure of their host states. In a more anarcho-Communism society those limits would not exist so those things that are currently prohibited to these communities, like the cultivation and processing of certian plants, would be up to the community to police.
At the same time each community would be responsible for their own protection. The reason being that just because your society decided in a non violence and aggression policy does not mean that those people who do not subscribe to those policies will not exist. Another thing to consider is that it is possible that people who would prey on those outside of your community could use your community as sanctuary.
These are the points that tend to break down any anarchy based societal group. The reason is these are the points that breed corruption into communism. The need for defense means the need for a leader for that defense organization. The need to discipline leads to the need for a set of rules, but the majority can choose to side step the rules in special cases, which leads an group of "More Equals" which leads the community towards statism and away from the anarchy based society.
Also there is no personal wealth in a communist economy. Everything is shared and needs are provided with excess consumables shared in an as equal as possible basis. Any accumulation of wealth would belong to the community not any individual. This excess would be traded with other communities for items of use to the community. So any wealth, ie something you can accumulate and not have an immediate need for, would stay in the community stores until needed.