What is a way to found a new country?There are two basic things that define a country.
1. It has to have it's own system of government.
2. It has to have broad international recognition.
The second one is very important as if other countries don't see recognize the government in place they will not deal with it, and an important function of a country is to represent itself and its citizens abroad. The most prominent example of this is Taiwan, where the government is not recognized by most other countries in the world because of Beijing's "One China" policy. As a result, the Taiwanese government has little or no say in international affairs and cannot properly represent its interests.
In today's world forming a new country really comes down to having a part of an existing country break off and form a new country. The most recent example of this is when South Sudan split from Sudan in 2011. It almost happened when Scotland held an independence referendum in September 2014, and it may happen in a number of places like Spain, where the province of Catalonia is split over the idea.
Currently, all worthy lands are claimed. So, to found a new country you should unite 2 or more countries, or divide a country (czechoslovakia is an example, two nations were founded: the Czech Republic and Slovakia).
You could invent and use technology to create habitable and self-sustaining platforms on international seas, and declare it as a new and independent State/Country.
Also, the micronations phenomena should be noted, but those are not officially recognized by world governments or major international organizations. More about: Micronation
First three things are relatively easy:
- Get some land. Get enough to satisfy the needs of your future country.
- Choose a form of government. A great one to start with is monarchy.
- Get some people to live in your future country. You can be your first inhabitant.
Now this is the hard part:
- Get recognition from other countries of the world. Good luck with this one.