Hi Kate,
Thanks for reaching out! If your users would like to be updated each time as events are added to your calendar, they can subscribe to your calendar’s RSS feed. This feed automatically refreshes with new details each time an event is published to your calendar, just like a standard RSS blog feed. You can learn more about RSS feeds for The Events Calendar on our Knowledgebase here:
https://theeventscalendar.com/knowledgebase/events-rss-feed/
For users who wish to download your events one month at a time, they can use the Export Events buttons that are located beneath your calendar pages. Clicking on one of these buttons will allow your users to download an iCal/ICS format listing of the displayed event(s), which can then be imported into the application of their choice. These buttons are detailed on our Knowledgebase, as well!
https://theeventscalendar.com/knowledgebase/exporting-events/
I hope that helps to get you started! Thanks again, and let us know if you should have any other questions!