A good way to relax when you're nervous about an introduction is to be prepared. With only a fraction of a second to make a good impression it's critical that you know exactly how you're going to handle it.
The good news is, you don't need to have a witty opening line, or canned conversation starters. Your first impression will happen before you even say a word. If you're not bantering clever remarks back and forth, how can you make a good impression?