Upvote:2
As soon as you notice your baggage has not arrived, meaning you wait for everyone else to get their luggage and nothing more comes out from the carousel, proceed to the Baggage Services counter.
Nearly all airports of size have one but it is sometimes closed when you arrive very early or late. In that case, find the service desk for the airline you travelled with and file a claim there. If for some reason it is closed too, you should go to an customer service counter for your airline. This can be at the same airport you arrived at but also an office in the city.
File a claim with them. Make sure you give them as much information as possible, such as your flight info and the square sticker with the suitcase tracking code (I don't remember the specific name). They will follow up with you at a later time. If your suitcase does not arrive at all or they cannot find it then it will be considered lost and you will be able to file a claim for some compensation (on most airlines) or with your insurance. Usually there is a limited time when you can ask for compensation which is why you must file the claim as soon as possible.