If you launched yEd from the yWorks website, you did not install yEd.
To install yEd, download the appropriate installer from the yEd download site and then run the installer on your machine. The installer will suggest an installation directory (typically C:\Program Files\yWorks\yEd) but you may also specify another directory (if you do so, it is up to you to know where yEd is installed). The installer will also ask whether or not it should create a desktop shortcut for yEd.
Hope this helps. Good luck.