A common trial / public speaking question: what do I do with my hands? How do I keep them out of my pockets or keep from waving them around?

Give them something to do. If you can’t think of a persuasive use of them, then give them the job of lightly touching your pants. Then they won’t move.

Most of all, make sure they, and the rest of your body, emphasize your message, and do not distract from it. Like so: