You're running it under Apache and MySQL and PhP, but GeoServer is Java based.
What you want to do is to install Jetty or Tomcat, and then drop the .war into the appropriate place for that software to run the code in. If you want to go the extra mile, you can use a regular web-server (apache or nginx) as a reverse proxy, so that you remove the :8080 port component of the URL.
Or you can use the standard Windows installer: http://docs.geoserver.org/stable/en/user/installation/win_installer.html
Edit from the future: You can also use Docker to run GeoServer, which is the modern way!