Many people have a healthy fear of speaking in public. The best way to overcome this is to NEVER picture your audience naked. Put yourself in the right frame of mind by thinking that your audience wants you to succeed at giving the speech. You generally want to start off with a little joke as an icebreaker and get them chuckling a bit. That will ease tension.
Frame it in your mind that your audience wants you to succeed. You want to smile when you're giving the speech because it gives you a sense of confidence. You don't necessarily have to look your audience straight in the face. You could look above their heads but look in their direction as this gives the illusion that you are looking directly at them. Above all else take a deep breath and slow down - not too slow - but at a reasonable pace. If possible don't memorize your speech. Just highlight the main points for yourself. If you want to memorize anything it should be the opening and closing. Impromptu speech topics often come from your personal experiences. It's helpful to provide a moral to the story - a modern-day fable.