When you have WMP running go to the menu items seen on the top bar and select the "tools" item. At the bottom of that drop down menu click on the "options" to open up a new screen. Then look for the "file types" tab and open that up. You simply place a check mark next to the file types that you want WMP to be the default player for and click the apply button before leaving.
This should see WMP start up automatically when double clicking on a wav, avi, mp3, or other checked file type. This also helps when placing an audio cd or dvd in a drive where WMP will start up right away for those.