It depends on whether your suffering performance anxiety or social anxiety. If its social anxiety then depending on how bad it is then I agree with randy talking to a professional about it can really help. A best friend of mine who i lived with for years had crippling social anxiety but after spending time with a professional you would never know now that he ever suffered with it. If its performance anxiety then the only real cure for that is performing. I know that sounds contradictory but its the only way. Every performance you do a little bit of anxiety will vanish, because you will get more and more comfortable.
If you are just starting out either in magic as a whole or starting out performing to people after spending time practicing effects it will be difficult, every magician goes through that. The first time I did it was in Convent Garden in London when iwas about 15, it took me hours to pluck up the courage to go up to my first person. I'll never forget it performed a ambitious card, hands shaking like you wouldn't believe, but i got through it. Once I did it i got a little bit of confidence, so going up to the next person was a little bit easier and so on and so on. By the end of the day and fears I had about approaching people had gone.
Don't be nervous about people saying no to you, dont take it personally, not everyone has the time to watch magic on the streets or just not really that interested. Dont worry about messing up, at somepoint it will happen, if you brush it off and dont make the situation awkward then the people you are performing for will be forgiving. And if you are doing it for free, then just see it as performance practice.
Trust me if its just performing you are worried about then you are making it into a bigger thing in your head than it actually is. Push yourself to do it and you will find that all the things you were worried about don't really mean much.