Travel is integral to my life. I start to relax when I walk in the airport and immediately relax when I board a plane. As a therapist, though, I know that more than 35% of the population experiences at least some anxiety about flying. 
Calm your mind by practicing mindfulness and meditation. Visualize a soothing environment, perhaps your destination, imagine and experience it using all of your senses. After returning from a trip to Bermuda several years ago, I started using this picture to help clients practice visualization. What do you see? (The blue of the ocean and sea rocks.) What do you hear? (The waves crashing, the cars passing above.) What do you smell? (Salt water and sunscreen). What do you feel? (The warmth of the sun, the sharp rocks, the firm sand, sunglasses on my nose.) What do you taste? (Fruit juice.) Choose a setting that is calming for you and immerse yourself in it using your imagination.
Even without leaving your seat you can relax your body. Starting with your toes and working yourself up to the top of your head, flex and tighten each muscle group and hold for a few seconds before relaxing. As your body relaxes, your breathing should slow, your heart will slow, you will have more oxygen in your blood stream, and you will begin to feel more calm.
Take slow, deep breaths. Fill your lungs to capacity before slowly releasing. Place your hand on your diaphragm and feel it pushing out as you breathe in and pushing the air out of your lungs. Make sure you get all of the carbon dioxide out of your system.
Think your way out of it. We have all heard the statistics that it is safer to fly than drive. Remind yourself that there are safety plans in place and your pilot is a professional, paying attention to the skies, not a distracted driver. There are many people working together to ensure your safety.
Distract yourself. Read a book, listen to music, work, talk to your neighbor, or watch the child squirming in his or her seat.
If all else fails, focus on the fear; notice it without giving in to it. Pay attention to how anxiety changes your body, including the temperature of your skin, your heart rate, the movement of your stomach, and the speed of your thoughts. Pretend you are a scientist making observations. Isn’t it interesting how our bodies react to our thoughts of fear? The more aware you are of what occurs in your body specifically, the more you can specifically address those symptoms and return to a feeling of calm.