If your luggage is found to be damaged on arrival in the baggage hall you will need to go to the relevant luggage handling counter at the airport (usually identified by the airline you have travelled with).
You need to ask them for a PIR form – Property Irregularity Report.
Please remember the airlines are responsible for the bags that they allow you to check in. The airline are then obliged to contact you to discuss the damage and their recourse could/should take the form of a new replacement flight cover, or compensation to the value of the flight cover. It may help if you take a picture of the damage at the time.