I am not the happiest of flyers. It's a quick way to get someplace, and something I have to endure. I used to be more than a bit stressed about flying. But, I have since educated myself, as much as possible anyway, as to the why's and wherefor's for flying. Once I realized that planes like a bit of turbulance I was a bit better. Then, I read a pilots description of his different flights. Seems they enjoy the more bumpy ones...and hate the smooth ones. I figure those pilots, co-pilots, and flight attendents aren't going to be up in the air as much as they are if they felt unsafe.
Now, when I fly, I tend to watch the FA's. If they are just going about their business, I'm good to go. I figure if they start looking worried, or stressed, then it's time for me to start worrying.
The other thing I found was that the plane really, really wants to stay in the air. It is a lot of work to land a perfectly good airplane. The plane is designed to be in the air. So, short of a terrorist attack or something mechanical going wrong, that plane is staying airborne. A terrorist attack or a mechanical failure are both things I can do nothing about..not a single thing.
So....get on board, try to relax. Bring some magazines to read. You're going to be great.