The term "conspiracy theory" is meant to be used as a semi-derogatory description of an unlikely explanation about a specific event. The term literally means a theory about a conscious plot to produce specific actions usually undetected by "the average person".
For example, there are many conspiracy theories about who killed JFK. The lists include the FBI, Cuba (on Castro's orders), Russia, etc. Yes he was killed, and Lee Harvey Oswald is implicated in the action, but depending which story you hear, he was either a patsy, a decoy, or under orders via whichever specific organization the story calls for.
There's conspiracies about the Pearl Harbor attack, secret organizations (which everyone seems to know about), connections with space aliens, secret plots from almost every organization, political group, business, actor/actress, alive or dead, etc., etc., etc. The only real connecting factor is that they are almost all fanciful and wrong.
Skipping the details, the question I want to discuss is: How do these types of stories get started to begin with?
In other words, how does someone learn about event X, and go from the "typical" explanation into making a wild sounding story? Not that the the "typical" explanation is always right either, but conspiracies, almost by definition contradict themselves. For example, if all the JFK assassination conspiracies were all believed, then he was killed by no less than 7 competing groups, and Oswald was somehow both a trigger man, and not involved at all.
The truth is, there are actually multiple reasons for these stories to come about.
I can't believe it
This is often a big catalyst. What occurs is so personally disturbing, that the person insists on proving either it didn't really happen (Elvis didn't die), or that it happened due to some long involved super secret government plan that's worthy of such a god-like figure.
The inability to accept what occurred leads to latching on some reported piece of detail and using that to prove the occurrence was impossible. They fail to admit that perhaps the news reported it wrong, or they simply didn't correctly understand the truth/science behind said detail.
Confusing accident for intent
This is a big source of the problem, and often related to the previous issue. It is easy to go back to reports, sound clips, videos, actions, etc. and assign premeditation to them, when in fact those actions were done just like most actions are: With very little forethought toward the future implications.
It is sometimes safer to assume there is a long-term master plan involved, instead of something as simple as "he just wanted to impress a girl". (Consider Hinckley's attempt to kill Reagan.)
I don't trust the media
I'll be the first to admit the news is often wrong for many reasons. And yes, sometimes it's either intentional on their end, or they are given false information and failed to learn the truth.
However, whenever a big story occurs, (JFK Killed, Pearl Harbor, 9/11, etc.) there are always those who simply assume the news is lying and feel compelled to prove it. They claim they are seeking truth, but instead they make the common problem of searching for details to prove a preconceived answer. And anything that threatens that preconception is proof of the "enemy" trying to cover the truth.
It's in my best interest
I'm going to combine two separate sources of conspiracies since they can be described by a single motive.
Quite simply, sometimes a person makes a conspiracy theory against someone/something simply because either: