Like any skill, I'd suggest this requires practice. One way I found as an introvert was to join Toastmasters. I don't have a big fear of public speaking—I can do it if I have to, but being in practice makes a huge difference. I've seen incredible improvement in people after 3 or 4 speeches.

Most clubs will have a social aspect and might gather for drinks afterwards. It makes a good way to practice smalltalk and keep in touch on a regular basis. There's usually a mix of people... some will be struggling with shyness and fear of speaking, others may be naturals and make good people to study for technique.

I've fallen out of regular attendance lately, but I'd highly recommend Toastmasters.