If you click into an appointment detail screen, you'll see at the bottom you have the option to either "Edit" the appointment or "Reschedule" the appointment:
This help doc is meant to help you understand the difference between the buttons and when you should use which.
One of the first things to determine is if the appointment you are looking at is for a class or for a service.
If the appointment is for a service (or personal reason), pressing the edit button will give you the Appointment Time & Date fields back to change the scheduled date and time of the appointment:
After changing the date and time here for the Service appointment and pressing save, the appointment will be rescheduled. You will not, however, necessarily know if the appointment time it was rescheduled for is available on the staff person's schedule. For that you should use the reschedule button which will present you with available timeslots to reschedule the appointment the same as if you went through "Setup One Time Appointment".
If the appointment in the detail screen is for a class, pressing the edit button will first provide you with a message to let you know that, because this is a class, you need to use the "Reschedule" button in order to move the class attendee from one class list to another:
You can dismiss this message if you don't care about the person being moved into another class roster and still just use the date and appointment time fields on the Appointment Detail screen to change the appointment time. If you do care about the class attendee being moved to another roster, you will need to press "Reschedule" instead in order to see other available class times the attendee can be moved into.