Don’t. Never, ever try to change the mind of a Moon hoax believer, i.e., someone who claims to be absolutely, instinctively sure that the Moon landings were faked in one way or another. It would be a waste of time: you can’t use rationality to dispel an irrational belief.
Debating a doubter instead can be very constructive. A doubter is still open to reasoned argument and to clearly presented evidence. Many people have doubts about the Moon landings simply because they’re not familiar with the subject and have heard the hoax theories. Since they lack the tools to determine who’s right and who’s wrong, they take the only sensible course: they remain doubtful.
There’s only one situation in which it’s worth debating a Moon hoax believer: in front of a doubter. A calm, well-documented discussion will often allow the doubter to realize that the hoax believer’s arguments are seductive but ultimately inconsistent and irrational.
However, some Moon hoax theories may seem quite plausible and convincing at first, and it’s easy to get lost in the technical details. What you need is something that clearly reveals the absurdities of these theories.
Here is a series of questions that in my experience are effective in rapidly exposing the untenability of Moon hoax beliefs. These questions force believers to justify their ideas with explanations that they cannot give without contradicting themselves. Moreover, they often produce a very intense and sometimes aggressive emotional reaction, which is worth a thousand pages of technical exposition in making it clear, to the doubter who observes the debate, who is rationally, serenely right and who is hopelessly, aggressively wrong.
These same questions, especially the first one, are also useful as a starting point for a debate with doubters. They force them to question the consistency and plausibility of their doubts, at least enough to want to know more about the subject, for example from the book you’re reading.
To avoid writing “he or she” repeatedly, I’ll assume that the hoax believer/doubter is male, which in any case is true most of the time. No sexism is implied; that’s just the way it is in my personal experience.