The Handheld Mic
The second type of microphone is basically a lectern-attached mic... without the lectern. Since you don't have a lectern to attach the mic to, you must hold it ― hence the name, the handheld mic. There are two problems with the handheld mic ― first, you must hold it; and second, you must hold it near your mouth. Let's consider how to deal with each of these problems....
Your first problem is holding the mic. Actually, for some people, a handheld mic is a blessing in disguise. If you're worried "what do I do with my hands?", holding a handheld mic takes care of that question ― one hand is always holding the mic, and so what you do with the other hand becomes much less of a problem.
But other people have the opposite problem ― they want to use their hands, and the handheld mic gets in their way. In this case, you might be able to use the mic itself as a prop. (But if you do this, be sure that you're not talking at the same time!) But otherwise, you'll just have to figure out a way to do everything you need to do with one hand.)
If that's gestures, that's OK ― one-handed gestures generally work just fine. but if you need to distribute handouts or do other things that require two hands, you're just going to have to work something out. (Unless one of your hidden talents is juggling, it probably won't be pretty.)
The second problem with a handheld mic is where to hold it. You've undoubtedly seen singers who use a handheld mic in their performances, and they hold the mic directly in front of their mouths, only an inch or two away, like they're about to eat it.
Don't do that! It's fine for singers who want the mic to capture every nuance of their voices. But you don't want that ― you simply want the mic to amplify your voice a bit. And holding the mic directly in front of your mouth hides your face from your audience, and the audience wants to see you!
So as a speaker (not a singer), you should hold the handheld mic about 4 or 5 inches below your chin. (If you don't have a ruler handy, that's about the same as holding an imaginary fist between the mic and your chin.) That's sufficiently close for the mic to capture your voice, but it doesn't hide your face. Even better, if you get in the habit of holding the mic in that position, the mic will follow you when you move your head, without even thinking about it!