In iOS7, Apple removed the shortcut for adding a calendar subscription to iCal on your iPhone. So here are the slightly more involved directions:
1) In your Full Slate account online, go to Schedule > More > Sync, Import & Export > 'View your Full Slate calendar in another application'. Copy the webcal URL on that page and email it yourself in a way that's accessible from your iPhone.
2) On your phone, copy the webcal URL that you emailed to yourself.
3) On your phone, go to Settings > Mail, Contacts, Calendars, then tap Add Account. Tap Other, then tap Add Subscribed Calendar. Paste the webcal URL into the link field.