Anarcho-capitalism is a philosophy wherein the sovereignty of the individual replaces the traditional, coercive institution known as the state, which imposes order in a centralized, top-down fashion. The word "anarchy" comes from the combination of ancient Greek words, "an" and "archon," which together mean "without rulers." Contrary to the modern, bastardized meaning of "anarchy," which entails disorder and misery, an anarcho-capitalist ("ancap") territory (whimsically referred to by many as "Ancapistan") would experience immense prosperity and happiness, with order being created in a healthy, competitive, decentralized fashion.
Self-organizing complexity is an emergent feature of systems that is seen throughout nature, with order arising through decentralized, local interactions. The above photo is an example of self-organizing complexity, as there is no alpha bird centrally exercising authority over the other birds and orchestrating the movements of all flock members; rather, order arises spontaneously, with each bird only paying attention to the behaviors of its immediate neighbors. Humans are no exception to the phenomenon of self-organizing complexity, and when free of top-down, centralized coercion, anarcho-capitalism naturally arises among humans. Anarcho-capitalism is based on the self-ownership principle, the notion that each person owns himself or herself and the fruits of his or her labors, and the non-aggression principle (NAP), the notion that it is always immoral to initiate force (violence in self-defense being perfectly moral, as long as it is not excessive) and engage in fraud against another person. Anarcho-capitalism can be succinctly summarized with "privatize everything" ("everything" as in services currently provided by the government that are both wanted and that do not violate the NAP).
Others have done excellent jobs making the moral case for anarcho-capitalism. Often, those who are persuaded by the moral case fall back on an ends-justifies-the-means rationale for remaining with the fundamentally immoral statist paradigm. They respond with one or more questions relating to the nuts-and-bolts operation of an anarcho-capitalist territory, and if they feel that a question or questions have not been answered satisfactorily, they often remain statists, despite having been persuaded that statism is immoral, which is very unfortunate. There have been various attempts to compile answers to the more common questions, but I intend for this site to contain an exhaustive as possible list of questions by allowing visitors to submit their own questions, which I will add to the common questions that I initially answered when I started this site.
The reader may be aware of numerous types of collectivist so-called "anarchy," and consequently wonder what makes anarcho-capitalism special, or the only system of true freedom. The various collectivist forms of "anarchism" have numerous fatal flaws. First, as the quotation marks indicate, they are faux forms of anarchy, since they entail the individual being ruled by "the collective," which, in practice, is just an elite group of rulers who are elected or command authority via charisma. Clearly, this does not meet the "without rulers" definition introduced above. Furthermore, life is experienced as an individual, and not as a collective: when you eat good food, or experience other forms of pleasure, these sensations are not telepathically shared with your friends, which makes the subordination of the individual to "the collective" immoral and nonsensical. It is also very telling that the most well-known form of collectivist "anarchism," "anarcho"-communism, is named after a system that is the very epitome of monstrous (both in size and degree of evil) government. Finally, "anarcho"-communism, "anarcho"-syndicalism, and so forth, with their built-in inefficiencies and warped incentive structures, would have serious scalability issues. In Ancapistan, a small number of such misguided individuals would be free to own land where they could live under one of these clumsy systems, but no socialist society would ever tolerate a pure free-market enclave of completely voluntary interactions. To summarize, anarcho-capitalism (and forms of anarchism that are virtually identical but merely known by other names) is the only system that wholly entails voluntary interactions.
It must be emphasized that many of the answers provided here are speculative and merely illustrative of how a particular issue could be effectively and efficiently handled in an anarcho-capitalist territory. An anarcho-capitalist society will be shaped by the aggregate intelligence, creativity, and decency of its members, and it is impossible to predict the precise details of such a society. Also note that many of the following questions are in the context of a future wherein Ancapistan coexists with nation-states. Obviously, we ancaps want a future wherein Ancapistan is the entire world. When this is the case, those particular questions will be moot.
My goal is to persuade you not only of the viability, but also the inevitable, incredible flourishing, of an anarcho-capitalist society. If you have a question that is not addressed here, then please feel free to send me your question, which I will add to the list of questions and answer. In order to be notified when questions and their answers have been added, please like this site's Facebook page.