You must set up the actual appointment slots before others can book them. Our NYU-licensed Google Calendar offers a quick and simple way to create appointment slots for your office. Enter their username in the 'Add Guests' field (to the right of the 'Title' field) How To Create Appointment Slots in Google Calendar.

a professor might add a TA to appointments for office hours, but would NOT add a student). 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. 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).