An unprovisioned order can usually be stopped.
IF THE INVOICE IS UNPAID
Simply do not pay it, and open a ticket asking for the order to be cancelled so it does not sit generating reminders.
IF YOU HAVE PAID AND IT IS STILL PENDING
Open a ticket immediately with the invoice number, saying you want to cancel before provisioning. If nothing has been spent with a third party, a refund or credit is normally straightforward.
THE EXCEPTION
A domain registration that has already been made cannot be reversed, even if the rest of the order is cancelled. Once the registry fee is spent, it is spent. If a domain was part of the order and has registered, you own it.
IF IT HAS ALREADY BEEN PROVISIONED
It is no longer an order cancellation but a service cancellation. Use Services > My Services > Request Cancellation, and see whether a money-back period applies.
ACT QUICKLY
The difference between a simple cancellation and a complicated one is usually a few hours. Open the ticket as soon as you realise, rather than deliberating.