The class in college that I can point to as the single class that prepared me the most for my career was a technical speaking and writing course I took as a senior.
The professor is a renowned curmudgeon in the department, but her heart is in the right place - she really cares about her charges and is somewhat ruthless in her criticism.
Every week we each had to give a speech. The first speech was just a quick 1 minute introduction; our final speech was a 15 minute lecture. Each speech was structured around a presentation; as most scientific talks are, and we were critiqued by our peers in the audience. Since our professor giddily pointed out our little foibles, especially uttering the filler words um, like, and and, our peers weren't shy about being starkly honest in their criticisms either.
Going to that class every week was an exercise in will power for me. Standing on stage in front of an audience of my peers - who may know more about my material than I - trying to appear intelligent, or at least coherent; I dreaded every moment of it until I was finished, at which point I would enjoy a brief sense of elation prior to starting to dread next week's speech.
The absolute worst part was waiting through the speeches before mine. My anxiety level was directly related to how many speeches I had to sit through before I could finally get mine over with!
The next worst experience was seeing other people stumble on stage as their physiology took over and their flight response screamed from within to get the heck outta Dodge. My empathy would mirror their emotion and make my stomach turn sour.
By the finish of the semester, our group had advanced remarkably. I was still anxious about speaking, but I could manage it much better. I credit our increased proficiency to our professor who honestly critiqued us and forced us to face the unpleasantness of learning to speak well.
The one lesson that I remember to this day from her was when she told us that prior to teaching each of her classes, she still gets butterflies - and she'd been teaching for over 20 years. That made me realize that the goal of overcoming anxiety when speaking isn't the true goal, the true goal is to learn to manage your emotions and project an air of confidence despite any quivering from your mid-section.
Fast-forward 10 years to present day when my wife suggested we join a local Toastmasters club. After joining, I soon learned that my confidence had waned in the years since practicing speaking in front of an audience. Well, what better place than Toastmasters to re-hone my abilities? The group is incredibly friendly and supportive - in fact, at first I was a little let down that they weren't as ruthless as my old college professor, but what they lack in brass they make up with in style.
A typical meeting starts with a joke or a speaking tip, followed by three 5-7 minute speeches. Each speech is then evaluated by a designated evaluator (which is a great skill in and of itself, combining public speaking, quick thinking, and polite critiquing). Afterwords, there is a Table Topics session where someone throws out a topic like, "What's your favorite camping story" and everyone takes turns telling their story in a 1 minute speech. Sometimes someone will instead start a fictional story, and then everyone takes turns adding to it. Finally, everyone votes for the best speech, evaluation, and table topic culminating in a nice little award to the winners.
There is a well defined structure that includes work books and speech topics that will take you from beginner to Toastmaster in 10 speeches. After you earn your Competent Toastmaster's certificate, you can choose a more specific path of speaking style, such as story telling.
The bottom line is, if you want to feel more comfortable speaking in front of your peers at business meetings, sales calls, or technical presentations, the only way you will improve is through practice. And remember, almost everyone feels acute anxiety when speaking in front of people, and even the most seasoned speakers don't loose that edge completely - they just learn to use its adrenalin boost to their advantage.
For some more information, check out my club's website.