To establish credibility, you can quote people who are experienced/educated in the subject. You can also include statistics for the subject matter and cite studies.
To establish your credibility when you’re giving a speech…
Trust your audience. Like your audience. Respect your audience. You may not agree with them. You may want to change how they think, feel, or act. But if you don’t care about them and their well-being, you shouldn’t speak to them. Want what’s best for your audience. Think of your speech or presentation as a way of benefiting them. Show them how your idea–your initiative, proposal, project, product, service–will help them solve a problem of theirs or help them achieve a goal that matters to them. Align with their values. Even if you want or, especially, if you want your audience to change their values, begin by identifying with them. Show people how the changes you want them to make — the new values you want them to adopt — affirm, refine, or advance the values they already hold. (You can simply tell them they’re wrong, of course, and that their values are all screwed up. Doing so may give you a pleasing sense of righteousness, but it will do little — nothing — to advance your cause.)
