As for the plot, well, they're in a big old mansion (one with a similar main floor layout to that in the game), a murder is committed, and it falls to the characters to figure out who done it. And, as the killings start to mount, it becomes something of a race to work out the solution before the killer strikes again. It is a lot to get done in the film's 87 to 96 minutes (I'll explain that in a minute), but the film manages it with aplomb.
As for that odd runtime length, when initially released to theaters, Clue had three different endings and depending on where you saw it, you got one of the three endings. Home video releases of the movie have featured a 'trilogy' ending that has all three tacked together with silent-film style cards explaining which is the one that actually took place. The Blu-ray (as, I believe, with DVD releases before it) give the option to play one of the three endings when running the movie or the trilogy version. All are amusing, but the one the trilogy ending gives as to what 'really' took place is certainly the best.
Many out there might argue that Clue isn't particularly well made, that it is full of bloopers and errors and logical inconsistencies. I wouldn't go so far as to use a lead pipe in the drawing room (or a wrench in the study) on such people, but I would point out that they're doing the equivalent of strangling the humor out of proceedings (perhaps with a rope in the conservatory or the ball room). Clue does have plot holes, logic flaws, and more than one not-quite-matching set of shots, but it's all so fast and frantic that to get upset by them you really have to purposefully try and stymie your enjoyment of the film.
By all this I am not suggesting that Clue deserves to find itself on any AFI list of best film or best comedy, but rather that it is an overlooked, under-respected, and a far too easily snubbed movie. It is fun and funny in a way that few films are and if you give it an honest chance, you just may find yourself part of the group of people who attempt to convince others of its genius.