Many people get easily fooled by cleverly laid-out conspiracy theories, as I have commented many times before (you can find all my related writings in the index page linked above.)
However, even though people get fooled, many of them are not fools, stupid or even uneducated. In fact, many people who believe in conspiracy theories are quite intelligent and smart. Their major problem is that they lack the necessary experience on critical thinking, an "instinct" so to speak, to spot fallacies when they are presented with them.
In my opinion this is a sad situation, where even intelligent and smart people are being fooled into believing falsities only because they lack the necessary healthy skepticism and critical thinking to avoid it.
How can people educate themselves to be more prepared to confront new conspiracy theories, and new clever claims of existing conspiracy theories? Here are a few tips.
(Note that this is not a set of instructions on how to answer the claims, only some tips on what you should consider before believing something you are told, no matter how alluring.)
Spend some time googling for argumentative and logical fallacies, and examples of them. It's useful to know them, as it helps spotting them.
Conspiracy theories often resort to a large number of such fallacies, and it's often a sign that the theory is not all that credible. (Well-researched and well-argumented studies don't need to resort to such fallacies to get their point across). This doesn't mean all conspiracy theory texts and videos contain such fallacies, but it's an extremely common feature to them.
Very typical argumentative fallacies include, among others:
Learn to spot these (and other similar fallacies), and consider an abundance of them to be a warning flag.
It's surprisingly (and sadly) common that people who believe in a conspiracy theory claim that they have "done the research" and "considered all the evidence", when in fact what they actually mean is "the author of this website has clearly done a lot of research on the subject, and it sounds credible to me."
In other words, rather than doing any research themselves, they are projecting (what they perceive to be) the research made by the conspiracy theorist onto themselves.
(These people are not lying per se. They honestly believe that they have "considered all evidence". What they don't realize is that they have been presented with extremely biased evidence and claims, and hence their conclusion is not well-informed.)
In some cases what they mean may additionally be that they have read more than one conspiracy website, and this somehow constitutes "doing research".
This is a very dangerous thing to do with respect to forming an informed opinion on the subject. When you read what a conspiracy theorist is writing, you are getting a highly-polished, carefully crafted, but ultimately extremely biased and narrow view of the whole picture. You are only seeing what the conspiracy theorist wants you to see.
Always remember that conspiracy theorists are seldom experts in the necessary fields to form informed and well-researched opinions (regardless of what the theorist himself or his pals claim) and that more often than not they have a strong bias. They may be quite skilled wordsmiths, being able to create alluring pieces of literature and video, and they are masters at making themselves sound convincing, but you should always try to see past the fancy words and bells and whistles.
Of course making some actual research is extremely laborious, especially on fields of science and technology which you have no expertise about. Fortunately you don't have to do it all yourself.
The most important thing you should always do when presented with a new conspiracy theory or new "evidence" of existing theories is to search for debunking websites. Preferably several independent ones.
This doesn't mean that you should automatically discard the conspiracy theory and believe the debunking. However, you shouldn't be automatically biased against the debunking either (which is sadly common among people deluded into believing the conspiracy theories).
What I do mean with this is that you should form an informed opinion on all available information, not just the biased cherry-picked information you get from the conspiracy theorists.
Often conspiracy theory debunking will be better researched, better referenced, better informed, will contain less or no argumentative fallacies and just plain make more sense. The explanations will also much better conform to the Occam's razor principle.
To some people the Occam's razor principle in science may feel like an "easy and lazy way out" (of having to actually explain how things really are). However, that's not at all what it is, in the vast majority of cases.
The Occam's razor principle is, simply put: If there are two suggested explanations for the same phenomenon, the simpler explanation is more preferable (as it tends to be more likely the true explanation).
There's another form for the principle: If there are two suggested explanations of about the same complexity, the explanation which covers a larger amount of evidence is more preferable. (To make the other explanation also cover the additional evidence it would have to be made more complicated than necessary.)
In this case "simpler" means "requiring less assumptions".
Example: When you come home, you see a muddy shoeprint on the floor. Let's propose two hypotheses on how it got there:
Hypothesis 1 makes a humongous amount of assumptions, not only about the situation in question, but about the entire Universe. The second hypothesis makes significantly less assumptions about the Universe, and hence is more logical and preferable. There's no reason to believe that the first hypothesis is more likely than the second one. (Moreover, the second hypothesis is testable, while the first one isn't.)
This is actually a very useful thing to do not only because of conspiracy theories but because of personal development overall. It's beneficial to know and to educate oneself on the subject of how science really works. This is because many people don't understand this, and thus are easily misled by unscrupulous people whose goal is to cast doubt on "the official story" and scientific research.
Conspiracy theorists (and many other movements) want to give an image of science as if it consisted of a few old farts who are stubborn and fixated on "established theories" and who outright reject anything that would contradict them, without even considering alternatives, and who are more interested in maintaining their personal world view (and, in some cases, maintaining their income) rather than uncovering the truth.
Science does not, and in fact, can not work this way, which is the beauty of the scientific method. Even if some people wanted to make science work like this, they couldn't. One of the main reasons why it's impossible is because of the world-wide peer reviewing process (performed by scientists all across the world, from different countries and cultures). There is no centralized "elite" group of scientists who decide in secret meetings what is the current "established truth" from which they cannot deviate. There is no, and cannot be, a conspiracy among scientists.
Healthy skepticism is also an integral part of science. Many people have a completely wrong notion of what "skepticism" means, and thus it's also something which one should study in more detail. (It does not mean "automatically reject new ideas", or any other such bias. Skepticism is not about bias. It's, in fact, the exact opposite.)