You can add a one-way subscription from Full Slate to iCal and a one-way subscription from iCal/iCloud to Full Slate, as follows:
To add a subscription to your Full Slate schedule in iCal, go to Schedule > More > 'Sync, Import & Export' in your Full Slate account. Then select 'View your Full Slate calendar in another application' and copy the URL there. Next, go to iCal and click File, then "New Calendar Subscription..." and paste the URL there. To then ensure the subscribed calendar will be available on all your devices hooked up with iCloud, follow these instructions: http://support.apple.com/kb/HT5029.
You can also overlay events from iCal and automatically block time on your Full Slate schedule if you use iCloud. To set this up, go to iCloud Calendar, where you should see a list of your calendars on the left side of the page. On the right side of each calendar name, there's a "share" icon that says "Calendar Sharing Info" when you hover over it. Click this Share icon, select "Public Calendar" and copy the webcal URL there. Now, in Full Slate, go the Schedule tab and click More > Sync, Import & Export. Choose 'Synchronize Full Slate with an external calendar,' then 'Add connection' and 'Subscribe to another external calendar' and paste in the webcal address.
These subscriptions update automatically every six hours, or you can update them manually by clicking Sync Now under Schedule > More in your Full Slate account. Alternatively, you might consider using Google Calendar as an intermediary to create a real-time, two-way sync between Full Slate and iCal:
Using Google Calendar to create a real-time, two-way sync with iCal:
First, establish a two-way sync between Full Slate and Google Calendar using the instructions here.
Next, establish a two-way sync between Google Calendar and iCal using the instructions here.
With these synchronizations in place, events will sync in near real-time in both directions, though you may need to refresh your calendar to see the updates in iCal. You can modify an event in iCal and it will update in Full Slate, and vice versa, regardless of where the event was originally booked.
Please be aware that anytime two disparate programs are connected, it's not possible to guarantee 100% accuracy. As a result, we recommend not fully relying on a sync or subscription to operate your business. The safest approach is to check your schedule directly on Full Slate, whether on the web or mobile.