Here's some sample code to get started. It's not for the exact section you wanted, but it will get you started on how to use the config API.

protected void _button_Click(object sender, EventArgs e)
    {
        Configuration configFile =
            System.Web.Configuration.WebConfigurationManager.OpenWebConfiguration("~");

        System.Web.Configuration.AuthenticationSection section =
            (System.Web.Configuration.AuthenticationSection)
                configFile.GetSection("system.web/authentication");
        section.Mode = System.Web.Configuration.AuthenticationMode.None;
        
        configFile.Save();
    }