The way I got over my public speaking jitters was by being a TA for highly unstructured discussion sections for ~6 semesters. I was given absolutely nothing to do with the kids, so I turned each session into an extended review/Q&A. Explaining basic concepts in my field 4 hours a week for 6 semesters to undergrads who barely cared enough to show up was excellent practice for talking in front of people and thinking on my feet. Not to mention I'm much less nervous, and I know what nervous reactions to expect.
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The way I got over my public speaking jitters was by being a TA for highly unstructured discussion sections for ~6 semesters. I was given absolutely nothing to do with the kids, so I turned each session into an extended review/Q&A. Explaining basic concepts in my field 4 hours a week for 6 semesters to undergrads who barely cared enough to show up was excellent practice for talking in front of people and thinking on my feet. Not to mention I'm much less nervous, and I know what nervous reactions to expect.
tl;dr Practice practice practice.