Here are the steps you need to take in the unfortunate event that you need to cancel an event.
1) Notify ticket buyers
Send an email to all ticket buyers using the Broadcast feature. Explain that the event has been cancelled, and, if applicable, when they should expect their refunds. You may want to think about what other questions people may have, and answer this in the email too, to prevent your ticket buyers responding with more questions.
2) Update your event status
Set your event status to 'Sales closed':
A popup will appear as shown below. Select the option 'Set custom status' and write 'Cancelled' in the text box as shown below. Add any useful information for customers, as this will appear on the event page.
3) Process refunds as soon as possible (if applicable)
It's advisable to process refunds as soon as possible. If refunds are delayed, or ticket buyers are confused about whether they are entitled to a refund, it can lead to your customers processing a dispute with their bank which can lead to a huge administrative burden for you, and if you lose the dispute, having to pay dispute fees on top of the refund. Learn more about disputes.
Refunds should be processed from Stripe or PayPal's dashboard (depending on what you use to process payments). From Stripe, it's a simple case of selecting the payments from the payments tab, and clicking 'Refund':