A while back I wrote a WordPress plugin for our church website that displays the This Week widget that you’ll see on the home page, and is also responsible for the What’s On page. It relies on the iCal Events plugin to download and parse an iCal feed from our Google Calendar.
It is somewhat tied to our particular setup (recognising our three churches and linking to the appropriate pages, for example, and the Europe/London timezone is also hard-coded). But it may be of some use to you.
Grab the zip file from below. forthcoming-widget.php goes in wp-content/plugins and activated in the normal way. Go to Appearance -> Widgets, add the widget and configure: