So I have a major phobia of flying. I've travelled all over the world and I still get anxiety whenever I get on a plane.
Part of what has allowed me to "conquer" the fear, so to speak, is that I am generally quite a logically-minded person. I KNOW that flying is safe - FAR safer than driving (actually, highway driving gives me anxiety too!) and I decided long ago that I would refuse to be paralyzed by an illogical fear. So even though I'm anxious and afraid, I made it non-negotiable not to travel. I can't even begin to describe what I'd have missed out on if I hadn't.
Now that that's out of the way, there are a few things I do. I make sure to take deep breaths and I repeat a word ("one") over and over in my head to stop the crazy racing thoughts.
If you're so inclined, you can tell a flight attendant that you're phobic, and they'll usually reassure you. You may also find that certain seats are better for you - I usually prefer to be at the front of the plane.
I also found this site very helpful. Every week they do a live chat where a pilot will answer your questions. I haven't done it in years but I found it useful when I first started travelling.http://www.fearofflying.com/
Also, exposure to flying helps. When I lived overseas, between our long weekends on holiday and flying for work, I think I averaged a flight a month for two years. While that's probably not feasible in many situations, doing it over and over did make me feel better about it.
(Strangely, I flew a lot as a kid, and only developed anxiety as a young adult.)
Hope this helps. You know what they say: feel the fear and do it anyway!