1) If you ever find yourself buffering on output, rather than making hesitation noises, just pause. People will read that as considered deliberation and intelligence. It's outrageously more effective than the equivalent amount of emm, aww, like, etc. Practice saying nothing. Nothing is often the best possible thing to say. (A great time to say nothing: during applause or laughter.)
2) People remember voice a heck of a lot more than they remember content. Not vocal voice, but your authorial voice, the sort of thing English teachers teach you to detect in written documents. After you have found a voice which works for you and your typical audiences, you can exploit it to the hilt.
I have basically one way to start speeches: with a self-deprecating joke. It almost always gets a laugh out of the crowd, and I can't be nervous when people are laughing with me, so that helps break the ice and warm us into the main topic.
3) Posture hacks: if you're addressing any group of people larger than a dinner table, pick three people in the left, middle, and right of the crowd. Those three people are your new best friends, who have come to hear you talk but for some strange reason are surrounded by great masses of mammals who are uninvolved in the speech. Funny that. Rotate eye contact over your three best friends as you talk, at whatever a natural pace would be for you. (If you don't know what a natural pace is, two sentences or so works for me to a first approximation.)
Everyone in the audience -- both your friends and the uninvolved mammals -- will perceive that you are looking directly at them for enough of the speech to feel flattered but not quite enough to feel creepy.
4) Podiums were invented by some sadist who hates introverts. Don't give him the satisfaction. Speak from a vantage point where the crowd can see your entire body.
5) Hands: pockets, no, pens, no, fidgeting, no. Gestures, yes. If you don't have enough gross motor control to talk and gesture at the same time (no joke, this was once a problem for me) then having them in a neutral position in front of your body works well.
6) Many people have different thoughts on the level of preparation or memorization which is required. In general, having strong control of the narrative structure of your speech without being wedded to the exact ordering of sentences is a good balance for most people. (The fact that you're coming to the conclusion shouldn't surprise you.)
7) If you remember nothing else on microtactical phrasing when you're up there, remember that most people do not naturally include enough transition words when speaking informally, which tends to make speeches loose narrative cohesion. Throw in a few more than you would ordinarily think to do. ("Another example of this...", "This is why...", "Furthermore...", etc etc.)
To expand on this... Spoken English should be treated as a separate dialect from Written English. They don't entirely share the same grammar, they have very different pools of idioms, and their concepts of effective use are almost entirely disjoint. Be aware that this difference exists, and practice your speeches out loud. Good essays generally do not make good presentations, and good presentations are almost universally terrible essays.
In particular, while Written English favors being concise, Spoken English favors explicitness, often to the point of redundancy. While a reader can go back and re-read a complex passage, and unpack it at leisure, during a speech there is no option but to parse it in realtime. Simple sentence structure, explicit large-scale structure markers, and outright redundancy are all markers of good Spoken English that your Written English instructors in school probably beat out of you.
Perhaps that's true, but I wonder about the great timeless speeches that also hold there own as essays. The Gettysburg Address, Churchill's speeches, JFK's inaugural address, Colbert or Jobs or D.F. Wallace's commencement speeches, etc.
Were they so good that they worked in both forms?
Or maybe they weren't good as speeches. I wasn't there for any of them.
Keep in mind that GP's advice isn't aimed towards well-practiced speechwriters and eloquent speechmakers. It's to people who are nervous even about joining Toastmasters.
Introverts can be really good at the "solutions rather than sales" aspect of interacting -- which is why we tend to do better 1:1 with people than in big groups.
When I give a talk or class in Israel, I can be sure that people will interrupt me, ask questions, challenge my assertions, and generally push me to explain what I'm saying. These interactions make things more interesting for me, always teach me something new, and (I believe) also make the conversation more relevant for other participants.
By contrast, my experience with American audiences is that they're much quieter and reluctant to challenge me during the talk. They'll wait until the formal question time at the end, and then raise issues.
And during the two classes that I gave in Beijing, participants were even quieter than Americans -- although the second group I taught (this year) were far more vocal than the ones I spoke last year, so it might have as much to do with corporate culture and their English level as anything else.
Bottom line, try to get a sense of the audience, and how they expect to interact with you. Then you can prepare an appropriate balance of prepared notes vs. discussion with the participants.
Over time, you'll get better at making these judgments and estimates; like everything else, public speaking is a skill that takes years to improve. But it's a real rush to give a good talk, and to know that you've taught others something that they didn't previously know. So do your best, and know that next time, you'll hopefully do even better!
I believe this is a crapshoot. Many times audience participation is more accurately described as "audience interruption and diversion". If you let them, a single audience member can easily derail a presentation in ways that all of the other audience members are not interested in.
Then grab that 1:1 attitude and run with it. You're talking about your favorite topic to just one person who is intensely interested in what you have to say, and will rarely interrupt you. This is where introverts excel, so be in that mental state. 1:1. Embrace it. And embrace the notion that just because that one intensely interested person is manifested as 2, or 10, or 100, or 10,000 makes absolutely no difference.
The same goes for the more modern 'laptop that is being use to display the presentation.' Hiding behind that can be a very easy trap to fall into.