The screenshots below show you how to get one or more links from your Google calendar(s) so that busy slots mark you as unavailable on Bookem:
Scroll all the way to the bottom to the Integrate calendar section and copy the Secret address in iCal format, as shown below:
Note: if you don't see the heading Secret address in iCal format then you're probably using a Google Workspace account. You'll need to get your Google Workspace administrator to follow the steps in this article to make it shareable.
Lastly, copy this Secret Address iCal URL to your clipboard and paste it into your Team Member preferences by going to Settings | Team Members | {your name}, into the iCal import URL. See screenshot below:
To find out how to do the reverse, i.e. how to sync Bookem with your Google or Outlook calendar, have a look here.