Though this is an area I'm not very familiar with, I believe that letting the applet write a save file to your local hard drive is merely a matter of granting it that particular ability via Java's security policy. This may involve signing the applet's JAR (all done with the JDK tools, so no need to buy a "real" validated certificate from Verisign). You might try the Applets forum here.
If you want to convert it into an application, you have to create a top-level frame/window to hold the components of the applet. This, again, is probably something many people in the Applets forum have done.
Writing that save file will be something more people can help with.