If a person has invented something and wants to patent it internationally, should he file a patent in each country or to an international patent organization (if any)?
There is no international patent. Each country protects IP under its own national laws and registration system.
However, there is the Patent Cooperation Treaty, which makes it easier to start the process in each of the countries that you eventually wish to patent an invention.
A typical route would be to file an application under the PCT, and then pursue national patent applications in each country that you plan to exploit your invention.
Patenting something internationally begins to cost a great deal of money and is a complex project with a lot of fact-based nuances.
Anyone seriously considering it should consult an experienced patent attorney for advice on where to apply first and which kind of application to file in that jurisdiction. Your application strategy might well vary based on the countries you are targeting, the kind of invention, the likelihood of success in getting the patent issued, whether the value of the patent lies more in its first years (many inventions) or down the road (e.g. pharmaceuticals that will undergo a long regulatory process), whether you need an issued utility patent sooner to sway investors, etc....