We've found Google Calendar to be indispensible for organizing our time and sharing our schedules with friends and coworkers. Now we can let others know about our preferred availability!
That's right! Set up blocks of time you'd like to offer as appointment slots. Simply click anywhere on your calendar and then on "Appointment slots." From there, create a single block of time or automatically split a larger block of time into smaller appointment slots.
Every Google Calendar has its own personal appointments sign up page; you can embed it on your website or give the URL to students and clients. You can find the URL for your appointment page at the top of the set-up page, which you can access via the Edit details link.
When someone visits your sign up page, their calendar is overlaid for convenience and they can sign up directly for any available appointment slot. When they sign up, Google Calendar conveniently creates a new shared event on both of your calendars.
Google Help on Using Appointment Slots