Clients are able to reschedule and cancel upcoming appointments by clicking on the Change/Cancel Appointment link in their confirmation email. That link is added into notifications by default, but can be removed in the Email Settings page if needed.
When a client clicks the Change/Cancel Appointment link, they’re brought to their appointment confirmation page, where they’re given options to cancel or reschedule. Granted that it is within your set time for cancelation or rescheduling, that is!
If a client deletes or loses their confirmation email, they can be sent a link to their appointment confirmation page (as seen above). This link can be found in the appointment details by clicking the cog icon and selecting Client’s Confirmation Page.
If an appointment is cancelled, it's up to you to refund your clients based on your business's refund/cancellation policy. You'll need to handle all refunds outside of Acuity in your chosen payment processor (PayPal, Stripe, Square, Braintree, or Authorize.net). Refunds cannot be issued directly inside of Acuity and will have to be manually processed in your payment processor's app!
Note: Time zones can't be edited after an appointment has been scheduled! You will have to cancel the appointment, then rebook with the right time zone in cases like this!