You must set up the actual appointment slots before others can book them.
Enter their username in the 'Add Guests' field (to the right of the 'Title' field).a professor might add a TA to appointments for office hours, but would NOT add a student). Did you know that if you have a work or school Google Calendar account, you can now create appointment.
When adding someone to the appointments, s/he will be invited to every appointment so only add people who will be assisting with all the appointments (i.e. Appointment Slots in Google Calendars - How to create. There are several things you can do with appointment slots: Note: Appointment Slots are currently only available to Google Apps users (i.e., not to personal Gmail users).