If you get nervous before a flight, you're not alone. On any one flight, there will be at least a dozen other people feeling the pre-flight nerves, so keep it in mind that it's a totally normal response. It can be distressing to have negative thoughts before and during a flight, but there are ways to combat it.
Trust the professionals
The airline industry is one of the most rigorous in the world, and every person involved in the process is professional. One of the main things that can cause flight anxiety is the perceived lack of control. If something goes wrong, then your life is in someone else's hands. It can be easy to take one accident you see in the news and start to get worried that the same thing will happen on your flight. The conditions of budget travel don't help the matter. If you're in an economy seat on a short-haul flight, then you'll most likely be in a fairly small seat with people on both sides of you. If you're already feeling nervous, then this can act to make you feel worse. A good starting point is to think that every pilot and air traffic controller has to go through years of training to be allowed to fly a commercial jet. Compare this to driving in your day-to-day life, where people with limited experience are allowed to drive on all roads when they have their license. To give yourself an idea of what pilots must do to qualify to fly, check out https://www.flyaeroguard.com/locations/austin-flight-school/, which may make you feel better.
Feel your feelings
Anxiety is something that many different people feel about many different things. Some people are anxious in small spaces, or at great heights. Others feel anxious about just stepping out of the door of their house. A common prescription for general anxiety which can help in all situations comes from basic meditation and CBT therapy techniques. This involves 'feeling' the feeling of anxiety and acknowledging it, rather than running away or getting carried away with it. Know that "I am feeling anxious," and then don't try to change that. This will create some space between you and the feeling, and will stop you from trying to get rid of the feeling, which will actually just make you feel worse.
Avoid drinking your way out of the situation.
A typical response to feeling nervous before a flight is to start drinking to ease the nerves. This can work but is often less useful than you'd think. Often, one drink leads to two, and then before you know it, you're drinking your third Blood Mary of the flight. This may help to ease your nerves, but trying to get off an aircraft while drunk is another thing altogether. If you aren't careful, you may find yourself in a worse state than if you hadn't drunk at all.