Contact the airline customer service desk immediately upon realizing your luggage has gone missing. The customer service clerk will ask for a detailed description of the bag and its contents. You will want to give as much detail as possible to help make the search go easier. You will then be given a claim number that you will want to keep for help in tracking your missing luggage.
Be patient and wait a little while for the airline to do its job. Your luggage is not going to reappear magically because you are standing at the counter yelling at the customer service clerk. Remain calm and check back about every hour to see if there is any progress with your claim.
Check online resources for details about the missing luggage. There are online resources, including Global Airline Resource Center (GARC), that work with the airlines to organize the tracking of missing baggage. To track your luggage you will need to have your tracking number, claim number or the phone number associated with your lost luggage claim. On the GARC website you will want to click on "track my luggage" and enter your tracking number in the appropriate section. Once the number is entered click on "track" and you will be directed to the tracking results page of the website with information about your luggage. If there is not a record of your luggage on this site, it only means the airlines have not contacted GARC with the details yet. If your search does not have the information about your luggage you should try to contact the airline's customer service department again.