First of all I have to say that you can't get rid of it from one day to the other. It's a longterm process.
Most people fear that the audience harshly evaluates them or even wants them to fail. This could not be farther from the truth. The audience wants you to succeed. When was the last time you saw a speaker failing? Not just a tiny stumble, I mean when they really struggled to speak. How did you feel for them? Right, pretty uncomfortable.
You can also fear that the audience notices you nervousness. Let's be honest, only you will see what's going on with your body. Even when your hands are shaking I bet not even the audience members in the front row will pick up on it.
You're your own worst critic.
Any minor flaws in your speech/presentation will most likely soon to be forgotten by members of the audience.
Having all that said: Here are some tips and tricks
1. Practice, Practice, Practice
I know a lot of people have already said that to you but it actually helps a lot. When you practice more you'll feel more confident with what you're saying and also get used to every fact and statement of your content.
You can stop practicing when you're so annoyed that you have to repeat it all the time but then do it three more times. Over-prep is the key to success!
2. Visualization
Imagine yourself giving a successful speech/presentation. Or even imagine yourself how good you will feel after your speech/presentation. It's finally over... It wasn't that bad actually. Whatever calms you down.
3. Get Rid Of The Tension
Hold your breath as long as you can, flex your muscles for 10 seconds, relax and flex again or you can do breathing exercises. 5 seconds inhale and 5 seconds exhale. It'll work. Trust me.
4. Don't Apologize
The audience will probably never notice it anyway.
5. Smile
If you look like the content matters to you, the audience will notice and keep track of what you're saying.
6. Don't Worry About Stumbles
Easier said than done but you should not expect it to go perfect. Everyone makes mistakes, that's what makes us human.
Finally, remind yourself that it doesn't matter what people think. Don't go in there worrying about everyone else. Go in there reminding yourself that you've done what you can and that no matter how well it goes you'll continue to get better.