Google Calendar can be used to show open slots in your practice schedule to potential patients. See the screenshots below.
Figure 1. A physician's practice schedule (the master schedule) or what
you can see. Make the appointment schedule as usual. Patient
information will not be seen on "the other side" of the calendar that
the patients subscribe to. Privacy note: the names in the screenshot
above are fictional.
Figure 2. Share the calendar with potential patients. Choose the option "Share only my free / busy information (hide details).
Figure 3. A patient-accessible schedule or what the patients can see.
Patients will see all open slots in your practice and can schedule an
appointment at a time convenient for them. Lunch time from 12 PM to 1
PM is blocked. You need to place a "subscribe to our calendar" button
on your practice website.