1. Look for inconsistencies in any story (and there always tons of them) and start harping on them, even if they mean nothing. Make ominous comments about "unexplained inconsistencies."
2. Disregard overwhelming evidence that disagrees with the conspiracy theory, or argue that it is alleged or unproven. Shift the burden of proof to the other side (you need only make an allegation, they have to prove you are wrong!).
3. Just make shit up. If someone tries to discredit it, then argue they are part of the conspiracy as well. This is a very convenient tactic, as the more people argue you are wrong, the more you can say that this is proof you are right! The very action of debunking a conspiracy theory is proof the conspiracy is real!
4. Wash. Rinse. Repeat.
As I have noted time and time again, conspiracy theories are the ultimate time-wasters and wasters of emotional energy. If you believe in them, they do nothing for you, personally (although I suppose the real conspiracy is the person who puts these theories out there - designed to get you all depressed and angry and to vote a certain way).
What is scary to me, today, is that conspiracy theories are no longer the outliers of wacko fringe thinking, but pretty much the mainstream of what used to be the "Grand Old Party" as evidenced by the goings on with the Texas governor - clearly pandering to the lunatics in his party. How sad!
So who believes in this shit? Mentally ill people, mostly. Mild or wild, you can spot a nutter from 100 yards away by his spouting of conspiracy theory nonsense. It is the ultimate form of externalizing as it puts the onus of all their problems onto someone else.