It takes thousands of employees to run a major airport. From the check-in agents and baggage handlers to security personnel and air traffic controllers, there are dozens of different jobs requiring a wide variety of skill sets available at airports worldwide. And do not just limit yourself to applying to the airport or airport authority. Scores of companies from rental car agencies to restaurants also hire people to work at their operations in airports.
Thoroughly research the jobs available at the airport you are considering working at. Start by investigating the employment section of the airport's website. Remember that new jobs will open up every week at large airports, so check back every week or two. Identify the jobs you are qualified for and interested in and make a list.
Send a carefully prepared cover letter and resume to the employer for each position you are interested in. Make sure to emphasize your related experience and present yourself in the best possible light. Follow up with each employer by telephone two weeks later even if you have not received a reply yet. Staying in touch reinforces that you are interested in and enthusiastic about the job and makes you more likely to get an interview.
Attend an interview for a position. Make sure to be well-groomed and professionally dressed and have a list of questions prepared for your interviewer (try to memorize the list, but it's OK to look at it if you need to). Also make sure to turn off your cell phone and remember to smile and makes as much eye contact as possible.
Follow up again with a courtesy phone call or email a few days after the interview. Indicating your continued interest can't hurt, and your enthusiasm might make you stand out enough from the other candidates to get you the job.