I fly quite a bit, both domestic and international, including the longest non-stop commercial flight in the world. Here's the best survival advice I can think to give a person in your situation:

Get to the departure airport at least an hour earlier than you need to. NightHiker pointed this out, and it will make a huge difference in your travel experience. Observe what others in line for security are doing and mimic them for the most part.

Eddie Murphy made a movie called "Holy Man". In it, he helped a guy deal with his fear of flying. Surprisingly, it is quite an effective technique, and the philosophy behind it is sound. A fear of flying, for whatever reason, is quite unrational, and I liken it to quitting smoking. When you are ready to accept control over your life, then you will be able to deal with what you cannot control a whole lot easier. Until then, you remain at the mercy of others, and under their control. Fear is part of life; something we can learn to control just like an addiction.

You control the decision of whether you will fly or not. Having made that decision, you also control how you will react to the event. What you cannot control is the outcome. Perspective is everything, and to fear flying anywhere more than you fear being shot or runover crossing the street or turning a corner is just unrealistic. Accepting the limits of our existence, and making the most of what we have while we are here is all any of us can expect from one day to the next. Realize this, and your life will be a lot more satisfying. Live in fear, and you are only wasting opportunities.