I read quite a bit of libertarian philosophy when I was younger, and never heard a convincing explanation of how you get private ownership of land, let alone things like the atmosphere, rivers, groundwater, etc.

Or pollution, are small amounts ok, as long as nobody can prove they are damaged? What if damage takes a generation, or only appears if lots of people are doing it? Diluting away the crap from burning a little oil is easy, when the whole world is doing it everybody is hurt.

Good question. Property rights are absolutely fundamental to libertarianism, perhaps second to the concept of self-ownership. Coming from classical liberal philosophy (most notably John Locke), the principle of self-ownership asserts that you own yourself, your labor, and the physical manifestations of that labor. Locke believed the earth was given to humanity in common by nature, but it required cultivation and effort to be useful. By "mixing" their labor (time, sweat, and skills) with raw land or resources, an individual removes the item from the state of nature and attaches their labor to it, making it their private property. Writers such as Robert Nozick and Murray Rothbard expanded upon this idea (Rothbard even went as far as to ground all ethics in self-ownership and property rights).

I want to ask you since I'm curious, the state simply declared ownership over territory and resources (and in some cases used violence to uphold it), why should you recognise any power in the state's part to do so? Likely many of the same justifications can apply to individuals as well.