While the details of each conspiracy theory vary, they typically involve attributing excessive power and influence to a small group engaging in nefarious activities. A classic example is the notion that NASA faked the moon landings. There are also many “false flag” conspiracy theories that range from the idea that the Bush administration was behind the 9/11 attack to the idea that mass shootings are faked to the claim that the pro-Trump stickers on the mail bomber’s van were placed to frame Republicans. There are also various medical conspiracy theories, such as those fueling the anti-vaccination movement.

There has been considerable research into why people believe in conspiracy theories. An intuitively plausible explanation is that anxiety and feelings of a loss of control lead to accepting such theories. Ironically, people who embrace conspiracy theories seem to be less inclined to act to counter the perceived conspiracy, perhaps because they feel helpless in the face of such imagined power. This is not to say that this always holds true—the conspiracy theory about Hillary Clinton running a slavery operation in a pizzeria led to a concerned citizen shooting up the place.
It is certainly tempting to embrace the stereotype of the conspiracy theorist: someone immune to logic, oblivious to opposing evidence and perhaps suffering from mental illness. To broadly dismiss conspiracy theorist using this stereotype would be an error, though it certainly does apply in some cases. My contention is that some conspiracy theorists use the same tools of logic and reasoning as everyone else and I will endeavor to show that this is true.
Since the world is a complicated place and is beyond the understanding of any one person, we all turn to experts when we want to know if something is true or not. For example, most of us lack the time and resources to investigate in person the nature of migration, so we must rely on (supposed) experts to provide us with (one hopes) true claims. Accepting such claims based on the (alleged) expertise of the person making the claim is to use an argument from authority. This argument has the following form:
Premise 1. Person A is (claimed to be) an authority on subject S.
Premise 2. Person A makes claim C about subject S.
Conclusion. Therefore, C is true.
This reasoning is inductive (the premises provide a degree of support for the conclusion that is less than complete) and its strength depends on the quality of the authority/expert making the claim. If the authority is qualified to make reliable claims in the subject area, then the argument would be a good one. For example, believing that this is what an argument from authority is because of my expertise as a philosophy professor who has taught critical thinking/logic since 1989 would be good reasoning, If the alleged authority is not qualified to make reliable claims in the subject area, then the argument would be a fallacious appeal to authority—the premises would fail to properly support the conclusion. For example, if you believed what I said about quantum theory because of my alleged expertise, then you would fall victim to this fallacy—my expertise in philosophy does not confer expertise in quantum theory.
Most people who rationally believe any theory believe it based on an argument from authority—the exceptions are those who are experts in the theory. For example, most of us believe in the theory of relativity because of Einstein and other scientists, not because we have done the research ourselves. In the case of conspiracy theories, believers often use an argument from authority: they believe the theory because an (alleged) expert has told them it is true. For example, those who accept the anti-vaccination theory point to the infamous paper that asserts a causal link between vaccines and autism or they believe because a celebrity they admire tells them vaccines are dangerous. Those who dislike Trump and believe that Putin has a urination tape as leverage probably do so because they heard the account from a source they want to believe. As such, for almost everyone the reasoned belief in a theory is the result of an argument from authority. So, then, what is the difference between the conspiracy theorist who believes that vaccines are dangerous because of what a celebrity says and a person who accepts relativity because of what Einstein said?
The difference, in general, is that conspiracy theorists tend to fall for fallacious arguments from authority as opposed to accepting well-founded arguments from authority. For example, believing that vaccines cause autism because of a debunked paper or because of what an actor says would be to fall into this fallacy. After all, unless the actor is also a medical expert on vaccines what they say about vaccines has no logical weight.
Resisting fallacious arguments from authority can be challenging, especially when the alleged authority is appealing, or the view being presented fits nicely with what one wants to believe. However, there are standards by which to assess an argument from authority. To be a good argument, it must be such that:
1. The person has sufficient expertise in the subject matter in question.
2. The claim being made by the person is within her area(s) of expertise.
3. There is an adequate degree of agreement among the other experts in the subject in question.
4. The person in question is not significantly biased.
5. The area of expertise is a legitimate area or discipline.
6. The authority in question must be identified.
If all these conditions are met, then the conclusion is probably true. However, since the argument from authority is inductive it suffers from the classic problem of induction: even if all the premises are true, the conclusion could still turn out to be false.