You can open a case from an appointment by clicking on the appointment in the diary and then clicking on 'Go To Case.' This is highlighted in red in the image below. Alternatively you can click on the appointment in the diary and hit G on your keyboard.
When you click 'Go To Case' it brings you to the case which you can see in the following image. You can see that some of the details are already pre-populated based on the patients record and the body site chosen at the time of booking the appointment.