Hello moiremusic,
Thanks for reaching out to us!
A direct link to the calendar is accessible via the “Events” link within the admin bar. If you’re using pretty permalinks, this URL will be http://yourdomain.com/events (or a different slug if you have the “Events URL slug” setting changed within the calendar’s General settings tab).
There aren’t any shortcodes or template tags that can be currently used to integrate the calendar on different pages, such as the homepage. However, I can suggest a third-party plugin that may be able to help get the calendar displaying on the homepage the way you are wanting.
I’m sorry I wasn’t able to give you a direct solution within our plugin, however I hope this was able to point you in the right direction.
Thanks!