Webstart is a method/technology to run applications without having to explicitly install them first. You do not need webstart to learn yEd. Simply download the normal installer, install yEd on your machine, and start yEd locally on your machine instead of webstarting it (if you have a hard time getting webstart to work).
Webstarting is usually done through your browser: when clicking on a link to a JNLP file, your browser starts javaws and passes the JNLP file to javaws. If your browser should ask you what to do with a JNLP file, tell it to open the file using javaws. (Browsers usually display a file chooser dialog for this purpose which you should use to select the javaws executable located in the bin subdirectory of your java installation directory.) The idea is that you as the user do not have to know about any of the details.
