See, the way it works is this: you want to know about the who, what, when, where, why, how of the conspiracy. Everyone directs to to the FAQ, claiming that all answers lie within. What you read in the FAQ is that NASA, not the government, is responsible for the conspiracy. They provide a link to another flat earth society thread where a guy speculates about how NASA could pull it off. Part of this speculation (not proof, mind you), suggests that you would be able to cover it up by paying off a grand total of 40 individuals world-wide. This includes high-ups in the NASA program, russian program, and chinese program. It also includes some (not all) astronauts and counts them only as half-people (I guess because anyone with actual evidence who is not implicit in the conspiracy would somehow be less likely to want to talk about how their years of training and lifetime dedication to becoming an astronaut were all based on lies--makes sense, I guess). It also includes a few other people.
They will suggest that other people in NASA don't need to be paid off because they don't have direct evidence--they just sit behind desks and see what the rest of us see. Of course, what they don't mention is that, even though they don't need to be "bought off," they still need to be paid, because, hello people, that's their job! People don't gain employment with NASA just for the love of sitting behind a desk and seeing what the rest of us see. And I imagine that these NASA control room people make a pretty good salary.
You will then go to other threads where they suggest that any university that is conducting research that verifies a round Earth is a part of the conspiracy or is conducting research using money that comes from NASA. Well, first of all, that is a lot of universities--including many, many universities that are not a part of the US, Russia, or China. It's also a lot of "fake research" that needs to be funded. The "Conspiracy Thread" never accounts for the vast sums of money that required to fund this research, nor does it consider that anyone who has ever looked through one of these huge university telescopes (more grad students than we can count) would have definitive evidence of either a round or flat earth that was every bit as compelling as an astronaut's evidence.
You will also find threads whereby it is suggested that all of the launches that NASA (and undoubtedly other space programs) conduct are staged. While these launches all have large audiences of people who come to see the liftoff, FEers will tell you that these launches are meant to dupe those people. The crafts don't actually go into space, but only pretend to do so, then land in an alternate location. The problem again is that the "Conspiracy Thread" never accounts for the cost of these faked launches in its figuring. Those fake launches still cost a lot of money in terms of building the crafts, paying employees, burning fuel, etc. There still need to be people manning both the launch site, and the alternative landing site. Since the people at the landing site know "the truth," they would then become people who needed to be paid off.
All of this operates under the absurd notion that you could pay a person off for the Dr. Evil-esque sum of $1 million. You know, "$1 million dollars isn't exactly a lot of money now-a-days. Virtucon alone makes $9 billion a year." If I were one of the 40, I'd think about...unionizing or something.
Anyway, this entire site and all the FEers on it rely on you not being able to navigate through the vast sea of convoluted arguments made here, and then actually put them together to realize how implausible their so-called "theory" is.
You just have to look at it as having fun reading some really ridiculous banter and leave it at that.