Shaking is a result of anxiety on your body so your body will go into a fight or flight response. During intense anxiety, your body is flooded with adrenaline/epinephrine. Adrenaline is pure energy, and your body shakes as a result.
So basically your excitement/nervousness over performing in front of people is causing your body to react with energy it's not use to handling and it compensates by shaking. The way to overcome this shaking is to have control on how your body is expelling energy. Deep breaths (make sure they are big, deep breaths) is a way of expelling this excess of energy. Another way to do it is to yell if you can find the appropriate way to do it (i.e. doing a street magic show and yelling "Hey everyone! Come check out this awesome show I'm putting on!"). Another effective way to expel this energy is to have fun laughing. A good mix of humor and playing around with the crowd can give you a good excuse to get in a good laugh and thus lower all the adrenaline your body is producing and will instead focus on producing endorphins which will make you feel good and happy during your performance.
It's really hard to get rid of anxiety before a show begins even if you have been doing it for several years. I get a little nervous all the time right before a big show. What I have learned from doing several performances over the last two years is how to channel my anxiety and use it to give me energy into my performance. Try to keep in mind that it's the magician that makes the trick and not the other way around. Have the crowd focus on your character and have your effects be an afterthought to the character. This takes less heat off of the mechanics in case you slip up and your audience will be more focused on the story you are trying to present to them. This also allows you to have more fun with your audience so if you blow a trick big time you can play it off as a joke and use another effect to recover.
An audience can pick up on when your really nervous so if you notice you are shaking, don't freak out! Instead slow things down with a subtle yet deep breath and focus more on the story you are trying to tell. If you can crack a joke or two and laugh along with the audience, this will help them to forget that you are nervous then you can go into your effect. Once you deliver the effect and let them soak in the moment, they are going to be entertained by your show and will not give a second thought to you being nervous earlier.
A good example of what I'm talking about is Kyle Eschen's performance on Fool Us with Penn and Teller. During the performance you can clearly see he is nervous and his body shakes at times. Whenever you see his body start to shake, you will notice he slows down his act for a moment and focuses on delivering a joke and uses the audience's laughter as time to collect himself. It's a beautiful performance of comedy magic that should give you a visual representation of what I'm talking about.
Hope this helps!
