Let me start with a disclaimer: I am not a psychologist. Read further only to learn how I'm afraid of flying yet I still manage to be a World traveler. Also, on the spectrum of fear, I'd say I land somewhere in the middle of "oh! Turbulence is no fun," and "I won't set foot in that death trap." Actually, I do have a moments of "I won't set foot.." but it's more along the lines of my general rule of thumb to avoid small aircraft like the plague. The fear isn't logical, I understand this, but it's nonetheless something that I have to deal with if I want to travel so here is how I've handled it:
1. Walk the Airport. The fact that the airlines want you at the airport so far in advance of your flight only leads to anxiety for those of us that fear flying. To clear the mind of the impending boarding, I leave my bags with the family and walk airport until it's almost time for boarding. Yes, it does result in several laps back and forth but on the plus side, I'm now pretty familiar with all the stores and restaurants in most major airports. This tip also doubles as a good way to help stiff backs as well as improve step-counts on step counters. Hopefully all the walking will help ease the anxiety and also make you tired before having to sit for a stretch of time.
2. Distract, Distract, Distract. Along those same lines, have a plan to distract you during take off, bearing in mind that certain electronic devices have to be stored away during take-off and landing. Whether it's music, audiobook, or downloaded movies, come prepared with distraction.
3. Something to Help You Sleep. Okay this is where I really want you to check with your physician but for me, I very rarely take any pharmaceutical drugs, prescribed or over-the-counter. This makes me a "light weight" so something as simple as a Benadryl can do the trick. Even if you don't fall asleep, it helps take the edge off like a glass of wine, but lasts longer and doesn't leave you dehydrated.
4. Sleep. Nothing passes time like a nap. Sleeping on planes is of course difficult and my family teases me because my mouth often falls open, but I'll take embarrassment over several hours of terrifying plane travel.
There are a ton of blogposts out there on learning to overcome the fear of flying by learning how planes work, safety measures, and similar logical-thinking solutions. However, I've known for years that there's nothing logical about my plane anxiety so none of that worked for me. This is all to say that my tips may not work for you so keep researching until you find what does work for you. I promise, it's worth it.