There are two types of public speakers: Those that get scared and those that lie about getting scared.
There is nothing natural about standing in front of a room full of people.
In my experience, your body and your brain do not get better at dealing with the fear over time. You do, however, get better at hiding your fear.
For me, the best way to overcome fear is to have committed to memory the first 1-2 minutes of my presentation (the first 180-360 words).
If I have been asked, at the last minute to do a 5-minute talk, you will see me furiously writing my opening lines. My first draft will be functional; it will get my point across and set the scene for the talk I am going to deliver. In subsequent edits, I will try and make the intro as exciting as possible.
If you can get past those first few minutes, your body starts to relax, and it's easier to think on your feet and improvise without a script.
It's also helpful, if you have time, to script word for word how you are going to end the talk (1-2 minutes). When you are ready to finish the presentation, take a pause, and just say two words that will give the audience permission to clap: "thank you".
Giving a talk is like flying a plane. The takeoffs and landing are the dangerous parts, so don't leave them to chance.