First, create an account in the Aurinko portal

When asked about the type of app you want to create chose 'Another API app':

Next, check 'Scheduler' feature for your new app (Mailbox API will be activated too).

On your new app's dashboard go to the 3rd todo item 'Check out your appointment booking page!'

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

Office 365 OAuth setup

Then review Booking API refs on how to create booking profiles.