Team America: World Police didn't seem a particularly libertarian movie. It seemed more like a movie just designed to flip Michael Moore the bird (not that there's anything wrong with that) rather than promote liberty.
As Ian says, find his buttons - everyone has one. My dad got riled up about the need for pubs to buy licences to have musicians playing, because it makes it so that certain types of bands can't play. The obvious answer is a free market with liberty. Anyone can start a venue of any kind, as long as they don't harm anybody else, and hire whatever musicians they like, as long as they don't infringe on other people's property (intellectual or otherwise). Getting government involved benefits nobody - the pubs have to pay more for a licence, they then can't hire as many musicians, and they have to increase the price of their food and drink, meaning that the musicians get less exposure. That part was really the foot in the door - libertarian ideas (like the legalisation of cannabis... and other drugs... and getting rid of any restrictions on them...) go down easier.
Once you can show someone how government force harms them, they are in the position of being personally affected. It's too easy to write off other people's concerns. I was asked the other day why I favour liberalisation of drugs - I don't use any illegal drugs. the answer is simple: I might want to, and I shouldn't be arrested and chucked in prison for doing so, and I don't want to pay to keep other people in prison. Drug prohibition concerns everyone. Government's use of force is wrong in most, if not all, instances. Get that message in there with a concrete example of where overregulation, criminalisation, "licencing" and all sorts of other government schemes screw up the pursuits of whatever one person wants to do.