To run Tile Studio II, you will need a PC with Windows XP or above. Since the program is still in beta, there is no installation program yet, it is provided as a zip file.
Extract the zip to a new folder and start Tile Studio.exe.
A little project file is included in the zip to play with, called Platform Tiles.ts2proj.
Try loading it. If you get an error about LUA52.dll, you will need to also install the
Visual C++ redistributable package for VS2013 from Microsoft.
You can easily add an icon to your desktop by right-clicking on your desktop, New…, Shortcut and then find the Tile Studio II executable where you extracted it.