Other writeups here have covered the basics. However, no one has mentioned the most important aspect of 'true' libertarianism - that in a libertarian system, your power is based on the amount of money you have - nothing else - and any property rights you might want (including the right to air, water, etc.) can be denied you by their owner.

Of course, as far as I know, most libertarians don't take such a strict, Objectivist view, as zeman points out.

So ximenez could buy rights to silence, clean water, air, etc. (Assuming he could afford them.) However, the tragedy of the commons zeman mentions would remain a problem, because water and air, and to some extent noise levels, most be owned in very large units. If zeman wanted clean air, but everyone around him sold their rights to it to a coal-burning power plant, the value of that company's right to pollute becomes extremely high - far beyond what ximenez could afford.

This leads us to the basic problem ximenez is facing - that even in an ideal market, it is inevitable that the market will give disproportionate (non-linearly increasing) power to larger accumulations of property and capital. When corporation A buys the rights to pollute all the air within 500 miles of ximenez's property, the market value of even 1 foot of (nearly) unpolluted air on his property becomes roughly equivalent to the market value of the entire package. This is an 'economy of scale' but it works against individuals in favour of vast corporations, and without the balancing force of government regulation, the tragedy of the commons effect will extend throughout any property type for which economies of scale exist - unless citizens act to secure their desired rights collectively - at which point we have a large corporation indistinguishable from a government, which acts to regulate air quality, or water quality, or whatever properties its citizens have collectively obtained.

A parallel misconception can be seen in the 'selfish gene' theory - there are always cases where larger systems are more efficient, and those systems will always be compelled to increase their own power - regardless of whether they are governments, corporations, or multicelled organisms - independent of the actions of any of the individual components of which they are made. Fortunately, for governments most countries have the checks and balances necessary to give individual goals the power to control the larger system. I hope we can do the same for corporations.