Libertarians and Anarchists are essentially the same thing at different ends of the spectrum, like Nazis and Communists.
Both believe the world would be better off without government. The difference is that Libertarians believe that with no government, people will act rationally according to their interests, and the economy will reward everyone according to their talents, while Anarchists maintain that with no government, everyone will rationally cooperate, sharing resources and taking only what they need.
Both beliefs are based on the false notion that people are fundamentally good and rational, and that government is unnecessary.
Libertarian philosophy is an anarchist philosophy, the minimum amount of government possible. Libertarians are anarchists, as are Marxists. The final phase of Marxism is that the national government, the dictatorship of the proletariat, would fade away leaving only the local governments, the local communes, therefore communism.
Of course, it was the failure of the dictatorship to fade away that doomed Marxism and communism.
Libertarians, unlike Marxism, don't have a plan for transitioning to the unrestricted free market. It is obvious from their theory that quite a lot will have to change for their vision to come into force. But the best that you can get from them is that the market and society in general will see the advantages of their vision and slowly the market and society will move toward the free market.
This becomes something of a problem though. Seemly no two libertarians can agree on what the final product of the vision will look like and how it will operate. They agree that they will have to a limited government to adjudicate disputes, specifically to enforce contracts and to maintain property rights. But they can't even agree on what constitutes property. They are conflicted over intellectual property, ideas, whether IP is legitimate property and whether their limited government should protect it. We are talking about patents, trademarks and copyrights.
This is not a trivial question. About 40% of the laws and regulations on the books in the US right now concern IP. A like amount of the civil suits are about IP. And most of the real money behind the libertarians comes from corporate sources, money that supports their think tanks like the Competitive Enterprise Institute, the Heritage Foundation and others as well as supporting the economics departments that are Austrian economics ones, Auburn, George Mason University, the City College of New York, etc. These corporations aren't supporting the libertarians so that they can eventually lose all of their intellectual property. The last estimate of the total value of IP in the US was 5 trillion dollars in 2008, six years ago. That was about 10% of all of the property in the whole country.
What I have found out when I question libertarians for details about what laws and regulations that their limited government will have is that they will have virtually all of the laws and regulations that we have right now. That the opposition to regulations is more against the idea of them rather than the reality of them. That laws and regulations covering IP, remember those corporate dollars, building codes, workplace safety, food and drug purity, child labor laws, anti-slavery and, of course, contract laws and laws establishing real property rights will remain in some undefined form.They are conflicted on environmental laws, workplace rules like work hours, holidays, vacations, etc., with most, not all, against them. The only law that they all seem to be against is the minimum wage.
They also seem to agree that property and resources belong to the first person who claims it. That there is no validity in the idea of property owned by the government that it can in turn sell to whom ever they want. If you are concerned that they want to give all of the US back to the Indians don't be concerned, apparently they have a white man work around that keeps this from happening. I just don't remember what it is right now and have no inclination to look it up. It is a guarantee that it is total bullsh*t, these are libertarians that we are talking about here.
This raises interesting questions involving the environment and pollution. The first claimant principle also applies to a company's ability to pollute the air and water. Rather than regulations limiting the pollution that a facility can release most libertarians seem to agree that production facilities that pollute should write contracts with the people and communities affected by the pollution, with people who moved into the area when the pollution was already being admitted will have to pay the facility to reduce the pollution. Only people who lived in the area before the polluting facility started up will not have to pay.
So in summary they don't know how we will transition to the self-regulating free market and they don't know what it will be like or how it will operate or how it will be different from what we have today. But according to them, cue the starry eyed gaze into a brighter future, it will be wonderful.
If these few explanations have left you with more questions than answers, you are probably not a good candidate to become a libertarian. I have found them to be singly unconcerned by the contradictions and the details of their philosophy, especially the economics side of it. Most seem to be happy that they will finally be able to legally buy drugs and that others are willing to fight their wars. Maybe that says it all.