First, create an account in the Aurinko portal.
Create your app, then сheck 'Scheduler' feature for your new app (Mailbox API will be activated too).
and authorize access to a calendar (in Google or Office 365 account that you own) :
Once a mailbox account (with calendar access) is connected click 'Download' to download your scheduler.html file.
Then open the html file in your browser, this is your appointment booking page!
To continue building your appointment booking app set up your own OAuth details:
Google OAuth setup
Then review Booking API refs on how to create booking profiles.