This was Orson Welles' last theatrically released film that he directed. It is a documentary about two con artists - Elmyr de Hory and Clifford Irving - but rather than talking about them specifically, it uses their stories as a way to investigate the meaning of art, truth, lies, forgery, expertise and most importantly, the cinema. Why do I say "most importantly, the cinema"? Because that is the true subject of this film - the making of film.
The first sign that this film is really about film is the fact that Orson Welles spends most of the film sitting at an editing desk, manipulating the film we are watching. Welles acts as a sort of narrator-raconteur-tour guide-editor-magician hybrid throughout the film, lending his own presence when no other footage could be had (much of the film is edited from an earlier, never-finished documentary, filmed by someone else - it was made on the cheap), and generally just explaining what it is we are looking at. Even when Welles is talking about things that have seemingly nothing to do with the cinema, like art forgery, it is still always related back. For example, his long rants about art forgery contain many, many jabs at the uselessness of 'experts' as any sort of preventative against art forgery, because they don't know what they are talking about. This is one of the key themes of the film - experts have no idea what the hell they are talking about. Their knowledge is superficial, and largely useless. While not explicitly stated in the film, this is a reference to film criticism, most specifically Pauline Kael's longform essay "Raising Kane", which attributed much of the success of the film to Herman J. Mankiewicz's screenplay, rather than to Welles himself. Kael wrote this essay as a sort of anti-auteurist experiment, an attempt to point out the fact that Welles did not, in fact, make Citizen Kane all by his lonesome, that lots of other people were involved as well. Welles did not take kindly to this essay and reacted accordingly. Whether this was because he liked being thought of as a wunderkind, or because Kael's essay attempted to point out the fact that many people were involved in the making of the film, but ended up claiming that Mankiewicz was the sole auteur, it is difficult to say, although it is notable that Welles did write a rebuttal article, that talked about all of the other people (besides him) who made Citizen Kane possible, although this could just have been an attempt to disguise his own massive ego.
Welles does spend some time in F for Fake discussing architecture, and how this is an anonymous and group activity, and how beautiful. Though he does not mention film in this section, it is clear that he is comparing the creation of a building to the making of a film (with its many contributors). Welles ends this segment with the line, "maybe a man's name doesn't mean that much," signifying the idea that the author is really irrelevant, but it is the text that matters. This moral is somewhat undercut, though, by the fact that Welles portrays himself in this movie as some sort of overlord of film - working the editing board, narrating from various places, interviewing and interacting with the subjects of the documentary, even telling a few stories of his own. The fact that this is so obviously a film "made by Orson Welles" is at odds with the idea that "a man's name doesn't mean that much" in art. This contradiction is almost certainly intentional, though, as one of the film's central ideas is to play games of irony with the audience - a sort of "how many levels can you spot?" type thing.
Another way in which Welles brings F for Fake back to film - Clifford Irving had written a fake autobiography on Howard Hughes. Welles links this back to Citizen Kane - claiming that the original idea for Citizen Kane was going to be a roman a clef about Howard Hughes, but they changed it to William Randolph Hearst because, "nobody would believe Hughes' life in fiction."
This is an interesting, enigmatic puzzle of a film. Fun and funny, but also thought provoking - even if most of the thoughts it provokes are of the, "what is the point of that?" variety. That is the game of the film - see if you can work out the point for everything.