How do you display different content for a page when user is not logged in

You could create a site-level content page ( telligent.com/.../24520.creating-content-pages.aspx ) with the widgets you want to show to anonymous users.

Then, create a widget ( http://telligent.com/community/developers/w/developer75/35323.getting-started-with-widgets.aspx ) for the home page with logic such as:

#if(!$core_v2_user.IsRegistered($core_v2_user.Accessing.Id)
 $core_v2_page.Redirect('URL_OF_CONTENT_PAGE')
#end

And place this new widget on the home page.  This will redirect anonymous users to your custom page.