As it says in the documentation you quoted:
Type premake4 plat, where plat is the name of the platform of choice. For Visual Studio 2008, this would be “vs2008”; for VS2010, this would be “vs2010.”
Just running it with no arguments (which is what double-clicking on it does) is not sufficient. You need to open a command prompt, cd
to the directory the project is in, and then run premake4 vs2008
(replacing vs2008
with the name of the platform you're targeting).
The most recent version of Visual Studio supported by Premake is 2010, so for later versions, you'll still have to use premake vs2010
- later versions of VS should still be able to load the project.