Google Calendar has an “Appointment Slots” feature which allows you to allocate increments of time you are available by appointment and then allows people you share your scheduling link with to self-schedule appointments as long as they do not conflict. When someone tries to schedule an appointment, you will receive an email invitation to that appointment and it will appear in your Google Calendar at the allotted time and no other users are able to schedule for that time period. If that appointment should be changed or cancelled, either user can delete the event from their calendar and it will mark that time block as available again. Note that replying “No” to an invitation does not mark that time period as free again.
You can use Appointment Slots in Google Calendar for much more than just Parent-Teacher conferences, and this article should give you enough information for you to use them elsewhere. You can view Google's help page on Appointment Slots for more information.
The process to schedule your Parent-Teacher conferences in Google Calendar requires a two major steps, first you must create a calendar for your conferences and then you must create your time blocks in that calendar when you are available. After that, you should be diligent about replying to conference invitations and deleting appointments if necessary.
Events created from Appointment Slots need a calendar to be created in. You should create a new calendar just for your Parent-Teacher conferences so that you can share it with relevant members of administration.
When your appointment link is sent out and students begin applying for time slots, you will receive Google Calendar invitations to your email. Each invitation will show you who requested the appointment and for what time. You have three options: