How do you found a new country?

So I'm kicking around ideas for a story I'm working on (Yes I'm writing again) and I had this thought: "How does a country form?"

I can think of a few ways: Conquest, International Fiat, Revolution.  Basically someone takes over something and calls it theirs.  The UN or other body "declairs" an area a country or a treaty says an area is a country.  Or the area is taken over from within.

Are these the only ways?

For instance if a group of people went out into international waters and created an island could they declare themselves an independent country?  Will a private group be able to go into orbit of fly to the moon and declare themselves independent of the Earth's nations? 

Honestly I'm not sure but I have a feeling if said country could defend themselves or had some sort of international leverage say a desired technology or commodity they could do it.  Especially if they're "just" a station or a small island.  Any ideas?  Suggestions on where I should look?