Many peoples' first instinct when encountering a too-paranoid 9/11 truther or an obsessive Illuminati alarmist is to shut them down immediately or to turn tail and run. I do neither. If you play it right, you're in for hours of free entertainment, and it's cheaper than a movie.
1. THIS IS ABOUT THEM, NOT ABOUT YOU
The first thing you learn when you hang out with hardcore conspiracy theorists is that they are the focal point of the universe. The government is after them, they're monitored while they piss, the lizard people have implanted nanobots in their brain, and in their piss, and they've taught themselves to drink their own piss, in preparation for the coming apocalypse, which is how the nanobots got into their brain. This is all information you can use. How? By asking questions that play into that paranoia. "Hey, isn't it strange that… Have you ever noticed… Did you ever think about who…" Make sure to relate every meaningless coincidence you can think of to both the threat of a global totalitarian government AND to what they ate for dinner yesterday. Make it personal. They love both the sense of danger and the attention, and everybody loves a curious audience, especially an egomaniac with a messiah complex.
2. EVERYONE IS DUMBER THAN THEM
This is a corollary of number one. An elaborate international conspiracy with cosmos-altering consequences would be very difficult to hide, yet nobody on the street is freaking out. Why? They only ever give one explanation: everyone is clearly stupid. Never mind the fact that the theorist in question survives almost entirely on TV dinners and Mountain Dew and that this is probably affecting his judgment. Besides, we all know about the mind-control chemicals in tap water. Mountain Dew is safer. To rev his motor, either A: join in bashing everyone but the two of you as mindless, television-numbed drones or B: play dumb, and allow him to "educate" you. Be warned: approach B will inspire so much irradiating smugness that you may be tempted to punch said theorist in his nanobot-infested nuts. You'll really know you're thumbing the button if he uses the word "sheeple".
3. THERE'S ALWAYS AN EXPLANATION
The conspiracy theorist is master of what I like to call the "rolling justification": any new data is conveniently incorporated into a giant, byzantine plot that explains why the FBI is responsible for the marketing of Doritos or whatever. All his neighbors bought new lawnmowers? Dorito conspiracy. Eggo recalled a whole batch of waffles? Dorito conspiracy. The trick is to keep this rolling justification going. Feed him new Orwellian nightmares that fit conveniently into the ones he's just conjured from the twisted depths of his fevered mind, but don't connect all the dots-- let him do some. He will experience a brief, cocaine-like high, and the impression that he's smarter than you will be strengthened-- he figured it out, not you. This can only be good for his savior complex, and saviors preach. Grab some popcorn.
4. FEED THE FIRE WITHOUT PUTTING IT OUT
Though you need to keep provoking him, you have to be careful not to seem either too contrary or too over-enthusiastic. If you're too over-the-top, he'll think you're patronizing him or he'll get jealous. Too argumentative, and he'll lump you in with the "sheeple". The key is a sort of dazed, slightly stupid fascination seasoned with bursts of excited intelligence. That way, you're learning from him. You're "just smart enough" to be his pupil, his padawan, his grasshopper. I know, I know. Try to contain your vomit.
5. DON'T BE TOO GOOD AT THIS
You always run the risk, if you manipulate the situation smoothly, that you'll seem too thorough a master of the intricacies of the Doritos conspiracy. Like you know a few too many secret chemtrail ingredients. Like you have too firm a handle on the latest UFO cover-up. If you manage to follow and fuel his rhetoric over-expertly, your hyper-paranoid prey may accuse YOU of anthraxing his Cheetos. Congratulations: you are now a member of the Illuminati. Intellectually impaired basement-dwellers everywhere are massing against you. Be afraid. Be very afraid.