First off, I personally just wouldn’t recommend going to that far with people who aren’t yet close enough to follow you. You’d need to be conversing with a really active mind to be able to actually get anywhere (not to mention you would have to be quite well versed in economics and social and political theory, as well as history, to be able to support yourself). I think it’s much more effective to make sure you never have to deal with that roadblock…as in, make sure that isn’t the question they ask when you pose that scenario (i.e. make sure whomever you’re talking to isn’t of the mind that is completely accepting of central authority).
And of course the way to do that is to have them go on at least somewhat of a similar journey you did to get where you are. Think about how you came to your own ideology and conclusions. What did you have to go through before you were comfortable with the idea of a stateless existence? For most people, the road is through the recognition of all the innate flaws and failings of government…and to a minarchist postition. Once you are there, it is much easier to take those next steps. (Much like what is discussed here.)
So as I was just talking about a few minutes ago on the subject of Ron Paul, you’re much better off (i.e. you’ll be much more effective) if you have them go through at least some of the linear progression away from large government before expecting to have any sort of success in a discussion of anarchy.
That being said, as a previous poster mentioned, the first easy answer of the kind you were looking for that came to my mind was Sowell’s brilliant “when you cut out a cancer, what do you replace it with?” However, that’s just a start, of course. Someone would certainly require more. So if you must go there, Kinsella wrote an excellent piece on this very subject which I highly recommend. It’s a bit combative, which you will have to curb if you wish to truly reach most people, but the argument is there, and it makes perfect sense…