The core code allows you to override the DNN skin.  This is all that the DNN site skin is doing.  There are 2 ways to override the skin.  First, by a querystring.  This is the method that is used to preview the skins in the Page Settings, Site Settings, and Skin Manager.  The other way is to set a cookie.  This is the method that the DNN site is using.  Upon clicking the icon, a cookie is set.  When the page reloads, the skin in the cookie is used instead of the skin that is specified in the Page/Site Settings.

function sizeLayout(size)
{
    setSkinCookie("DotNetNuke_Skin_Layout_Size",size, new Date("December 31, 2010 23:59:59"),"/");
    location.reload();
}

function setSkinCookie(name, value, expires, path, domain, secure) {
  var curCookie = name + "=" + escape(value) +
      ((expires) ? "; expires=" + expires.toGMTString() : "") +
      ((path) ? "; path=" + path : "") +
      ((domain) ? "; domain=" + domain : "") +
      ((secure) ? "; secure" : "");
  document.cookie = curCookie;
}