Rule #1 : Don't cite Wikipedia
Rule #2 : DON'T cite Wikipedia
Read a few books and pamphlets regarding classical liberalism, since socially speaking, it has most in common with the Libertarian ideology. Don't do cheesy one liners unless you can expand on them immediately, and if they have something to do with the subject you are approaching. The Libertarian manifesto is almost entirely an economical one, so unless you have some knowledge on how the markets actually work, what inflation is, and how the Federal Reserve works in America, then don't do it.
As well, don't paint it in rose tinted glasses as it is the most surefire way to invalidate your presentation due to bias. Take a professional approach to this entire matter, citing sources, facts, and studies regarding what you are talking about, offering breaks in the presentation to explain, more in depth, certain facets of either the movement or economical terms and what they represent in order to keep your audience on the up and up. Compare it to other economical systems, such as the Fascist / Communistic government ran / centrally planned economies, and the current modern day Capitalist economic model of government regulations.
Don't sugar coat it. Libertarianism, like Fascism, Communism, Anarchism, Monarchism, etc all have their pros and cons. You will be taken more seriously if you don't ignore the downfalls of your ideology and people will be more willing to listen to those that can admit their mistakes or don't attempt to make them seem smaller than they truly are.
Most important of all, do your goddamn research. If this ideology actually means anything to you besides a fad, you will do your utmost to research the topic from all angles, listen to any opinion presented to you, be it that of a supporter or a dissenter of the ideology, and form your own personal opinion on the subject. Parroting is the death of the liberty you hold so dear.