I have written in the past How Doctors Can Use Google Calendar to Help Patients See Their Practice Schedule and Make Appointments and How Patients Can Monitor Their Medical Condition with it.
The screencast below shows how to make a public Google Calendar and embed it in your website:
Screencast: How to make a Google Calendar public and embed it into a website, by by @jasonhbuck.
Google Calendar for Doctors: Help Patients See Your Practice Schedule and Make Appointments
Google Calendar for Patients: Monitor Your Medical Condition