Ensure that the airlines are able to find you by labeling the outside and inside of your luggage.
Put additional identification inside your bag including a copy of your itinerary. This can help the airlines know whether to send your bags to your travel destination or your home.
Also, no matter what kind of rush you are in never leave the airport without reporting lost luggage.
If your luggage does not arrive in the baggage claim area, find the baggage agent on duty immediately. There’s a chance your luggage already arrived and is locked up in the agent’s area for safe keeping. Sometimes luggage is loaded onto a non-stop flight even though you were on a plane that had a stopover on the way so your suitcases get there before you. But if your luggage is not there, do not leave the airport before completing the paperwork for the baggage agent. Fill out all information about your luggage on the forms provided.
For all the traveling I’ve done my first suitcase was lost last year and until then I didn’t think it could happen to me. Always plan as though your luggage will arrive late (or not at all) and bring an emergency hygiene kit and snap a photo of your bags to show the airline agents and save time when reporting the loss.