Anarchism is the belief that people can organize themselves without having someone tell them what to do. Anarchists believe that it is better for everyone to have a direct say in how things should be done, instead of having leaders or bosses make decisions for them. Anarchists also believe that participation should never be forced by other people.
Contemporary anarchy works on non-hierarchicalal tenets and based off of consensus and direct democracy. Networks (like this or this) are setups of collectives. Collectives are set up in boroughs and towns and cities representing that area, or as working groups with a distinct purpose to fulfill (such as food or a region wide newspaper). Affinity groups in those cities and towns meet and form those collectives.