What would an anarchist world look like? How would the people currently in different "nations" around the world relate to each other? Anarchism itself is a group of ideas that has a great many branches, perhaps more than most memeplexes, because its inherent lack of respect for authority usually keeps anarchists from blindly following the ideas of history's past anarchists. So would all anarchists agree on what an anarchist world would look like? Very unlikely, but the following is what "my kind" of anarchists would imagine anyway.
(For introductory information, see also Anarchy is Order and decentralized democracy.)
If a group of people want to live without much technology (such as the Amish), or with others who dress all "goth", or within a community where everyone understands sign language, then they are free to have and live in that "atomized" community. However, the individuals within these communities are also free to randomly move to any other community if they so choose. Both the communities and the individuals operate on the principles of self-determination.
Non-Anarchism in an Anarchist World
If other people want their own little community of capitalism, or monarchy, or slavery, then they are also free to have it, so long as everyone in that community is there of their own free will. However, if anyone in that community ever decides they don't like being a slave, serf, or wage slave anymore, then anarchists would help them free themselves. If 99% of a community's inhabitants decide they don't want to be wage slaves anymore, leaving only the CEO and board of directors, then anarchists would help free not only 99% of the people there, but 99% of the means of production as well.