I concur with Toastmasters International being a great place to start. I joined Toastmasters because of a recommendation from a very important man who told me how much it had helped him. It helped me to get over the fear of public speaking. Now I've gotten comfortable with it and pretty good and usually win
Best Speaker or
Best Table Topics wherever I do go to various meetings. I then started setting up speaking engagements to promote books I've written and other info products I've created. My first venture outside of Toastmasters was speaking at drug rehab and AA meetings (unpaid). (No I've never even tried drugs and never been a drinker but have written self-help, motivational books that are apropos to the topic.) But I felt it was a good place to start and allowed me to get my feet wet. It's not a full time career but I've done paid Public Speaking.
If you check out
http://www.learningannex.com/ they have some good classes on the subject.
Easiest way to start is to do your own P.R., local papers often list "events" at no cost. Post flyers on bulletin boards and in targeted areas to reach your market. It's also fairly easy to get on local radio shows who are always looking for guests. If you can talk about the subject well you'll get free publicity and the chance to give out your number so people can pre-register for your event. Get them to call first if interested. Once you have enough interest, then get your location (community centers; churches; parks; hotel rooms or even a local store, salon, bookstore, diner, etc. that will host your event. Some will do it for FREE especially smaller diners that aren't that busy anyway and know that guests will buy food and drinks.)
If you have something to say or teach and promote it right people will show up. You can charge very little up front initially or make it a free event then sell them your follow-up stuff in the back of the room. Works well.
Good topics to speak on:
Motivation, self-help, positive thinking
Community Activist Issues
Relevant Political topics
Relationships
Parenting
Credit
Work from home opportunities
Avoiding Scams
Avoiding Foreclosure
Alternative Approaches to finding employment
Self-Defense
Investment Opportunities
Immigration issues
The subjects of self-defense; home-security; identity theft; cyber crimes; rape prevention; etc have worked well for me because it's easy to appeal to people's fears and desire to be safer.
Actually ANY topic is good IF you have some useful, valuable knowledge, experience or expertise in it. It's all about being able to find your market and getting them to show up. If you find them they will come (at least enough of 'em to make it worthwhile) ...regardless of the niche.