Hi Pieter,
Thanks for your interest in our plugins! You can export events from any view or any single event page. On view pages (like the Month View) clicking the Download button gives you an .ics file. Single event pages have Google Calendar Export and iCal Export buttons.
I recommend that you check out our demo site at WPshindig.com to see the buttons in action. You can also download our free core plugin, The Events Calendar, and play with it on a test site.
Cheers,
Leah