Toastmaster here. Joining Toastmasters was one of the best decisions I've ever made. There are over 10,000 clubs worldwide (check out:
www.toastmasters.org) and probably 3 in your town that you never knew about. The only problem with Toastmasters is that they need to change the name.
The meetings open with a quick introduction and then 2 short (3-5 min), prepared speeches, and then what they call "table topics" where they give you a random topic and you speak about it for 1-2 minutes. Then people evaluate your speeches and give you pointers. Then at the end of the meeting (depending on the club), they give awards for best speech, best evaluation, and best table topics. Anyway, that's the general form and there are other roles as well (joke teller, timer, etc.), depending on the club. The schedule is determined in advance so you know what your role in the meeting will be beforehand. The goal of the meeting is to give everyone at least a brief chance to stand up and speak in front of the entire group, either as a speech-giver, evaluator, table topic, or joke teller.
In med school, my public speaking skills really came in handy and I know it'll mean even more for me in residency. I actually volunteer and look forward to giving presentations now, whereas it used to make me sick to my stomach.
Needless to say, I highly recommend the Toastmasters experience!
