A persuasive discourse is a formal speech intended to persuade listeners that the speaker's opinion on an issue is correct. It follows the structure of a persuasive essay, with an introduction that includes a grabber and thesis statement, a body with three arguments supported by evidence like statistics and examples, and a conclusion with a summary and clincher. Effective persuasive strategies include keeping the speech short and simple, repeating key points, using transition terms, and asking questions, while ineffective techniques are reading from notes, standing in one place, focusing on only a few listeners, and avoiding eye contact.