The reason why most people think libertarians are a bunch or cranks and cooks is exactly this: most libertarians suffer a complete inability to see reality and to find practical ways of doing things... not really (laughs) it is just that a good idea is sometimes an unpopular one.
Although it would be nice to live in a world where charities could manage parks and other non-revenue generating activities most people are not behind us. It would require a fundamental change in the way everybody thinks about parks and would be a lengthy transition. The good news is that it is practicable for parks to be privately managed because there is more than one.
However, when it comes to the transportation system that is an issue so complicated that it would take a book (thank you Wes, for the recommendation) to fully understand how such a system would work. I have not done much research into the issue, but I would wonder some key things: where does the money come from (tolls?); how would we prevent monopolies or exploitation? (usually the government handles monopolies because competition is impractical)
Keep in mind that neither party fully supports these ideas. We libertarians have such good (and populist) ideas: balanced budgets, leaner and more strategic foreign presence of our military and a different tax structure (Can you have a progressive tax structure without having to give up so much information?) However: when people hear ideas such as closing public libraries and schools: they think we're anarchists and are scared to the two parties.
Also: EVERYBODY uses the transportation system. I don't know anybody who hasn't done one of the following: walked/rode on a sidewalk, walked/drove/rode on a paved road, rode a subway/bus/train (I myself have done ALL of the above) so shouldn't EVERYBODY help pay for it? Everybody eats too, but we all eat different things at different places in different amounts, but we all use the SAME transportation system.
The books Wes recommended are linked here:
Alex's concern about monopolies prompted me to write the following comment, because monopolies are an important phenomenon for libertarian economics to address.
You've got a lot of great thoughts in your comment- to hit on just one, your concern about monopolies brings up a bigger question, which is what causes monopolies? I actually think an unregulated market would be much more free of monopolies.
In fact, I believe it is only by an act of coercion (e.g. government regulations, subsidies, etc.) that a true monopoly can be established, not due to a lack of regulation or the operations of a free and unconstrained market.
To use an example in the field of transportation, many cities regulate the number of taxis by requiring them to get a license or "medallion" to conduct their taxi business (of which there are usually a limited number, or for which the price is usually prohibitive). As a result, there are fewer taxis, with lower quality, and higher prices because they are protected from competition by the government- they have a cartel or a monopoly.
It's actually very interesting that you are concerned about monopolies in a free market for transportation, because this is an industry that is rampantly subject to the inefficiencies of monopolies due to the heavy government regulation thereof. Indeed, I'd say the biggest, baddest monopoly on transportation is the government and its special interest private contractors.
Ayn Rand has some great, succinct thoughts on monopolies here:
P.S. This is a critical part of Alex's analysis: "However: when people hear ideas such as closing public libraries and schools: they think we're anarchists and are scared to the two parties." That is exactly right.
As defenders of libertarian thought, we have to understand that this is the kind of feeling people get when we discuss our ideas, and we have to learn how to address these feelings. To me, it should be the other way around. If someone suggested nationalizing the shoe industry and centrally running it with taxpayer money, people would scoff and call them a communist.
How are shoes and books different? Or shoes and education? Or shoes and transportation? They are all goods that we value highly and have powerful economic incentives to build industries around. The market that's done so well at distributing shoes (so that even the poor among us can easily afford a pair) can do just as well at creating and distributing the world's very best transportation, education, and books.
Tying it in with monopolies, a government monopoly on education or transportation simply cannot deliver the quality or price that a free, unfettered market of enterprising individuals can. We as libertarians have to help people see that society wouldn't fall apart without socialist education, just as it hasn't fallen apart without "socialist shoes" or "socialist fast food."