You can create blocks of time on your calendar designed to let others reserve an appointment with you. These are called Appointment Slots in Google Calendar. For example, professors can invite their students to reserve time during office hours each week. More detailed instructions can be found on Google's Documentation page.
Creating a new appointment slot block
You can only create appointment slots while viewing your calendar in the Day or Week views. Make sure you are viewing your calendar in a web browser on a computer and not using the Calendar mobile app.
Highlight the block of time you wish to make appointment slots.
When the event window pops up, choose Appointment slots out of the row of options below Add title. The event window will change.
The default will be to have multiple slots set to 30 minutes apiece. You can change this timeframe, or you can also choose to have the whole block of time be a one-time slot by clicking Slots with duration and choosing Single slot.
Set the duration you want your time slots to be, enter a title for the appointment slot block, and choose what calendar you want your appointment slots on (the default is your personal calendar).
Click More options to set up recurring time slots and add more information such as location or description. Then click Save.
Invite others to reserve an appointment slot
Once your appointment slots are saved, click on the block of time again to see the event detail pop-up.
In the pop-up, click the link that says Go to appointment slot page for this calendar.
A new page will open in another tab in your browser. That new page is what others will use in order to schedule one of those slots you just created.
Copy and paste the appointment page URL link from your web browser.
Share the URL link for that page with anyone you want to reserve an appointment slot.
As a note: when you look at the appointment slot page for your calendar, you will also see all of your other appointments and events - that is because you are the calendar owner. Others will only be able to see what they have been given permission to see, which may only include the appointment slots you've created.
Tips and helpful information
More than one person will be able to reserve a single block of time if it has not been approved by you yet.
A scheduled time slot is only officially approved when you respond yes to the meeting request.
Both you and the individual can change your meeting response to no, or delete the meeting, at any time.
This removes the time slot for the individual you are meeting and opens that time slot back up on your calendar.
You can edit appointment slots at any time the same way you edit events on your calendar.
All edits made to your appointment slots are automatically reflected on the appointment slot page for your calendar, so you do not need to re-share the link to your potential attendees.