Exposition Intuition

As You Know, Speculative Fiction often relies on large quantities of Expospeak in order to deliver enough information to the audience that they can work out what is going on. When the hero is Trapped in Another World or some other sort of Fish Out of Water, he will often be provided with a companion almost immediately who is of this strange world, and therefore can serve as Mr. Exposition. On the other hand, when the series is based around Imported Alien Phlebotinum, it may come with a comprehensive user's manual, or an alien visitor (in alien invasion series, especially an alien defector) who can reasonably act as a source of information.

And then on the other other hand, some shows just, well, don't care. But we're still going to need that Expospeak. If the audience doesn't have it clearly explained to them what the aliens' plot is and how their Applied Phlebotinum works, they might not realize how clever the writers were—what do you think this is, Battlestar Galactica?

But if he doesn't have the special backstory to justify his insider knowledge of aliens, monsters, interdimensional beings, vampires or mole people, how would Mr. Exposition be able to explain what the bad guys want here or how they work?

Well, let's just declare that he's a Scientist. We all know that being a scientist is basically just science fiction speak for being a wizard, and it means you have magical foreknowledge. We'll say that because he's a scientist, he can tell, just by looking, that the twenty-story tall monster must gain his great power from a form of fusion energy, and is obviously weak against low temperatures, and will be attracted by the soothing sounds of John Tesh music.

Sure, he'll couch it as a "guess", as if he's just making a perfectly natural extrapolation based on what he's seen and real science. But his "guess" will be incredibly specific, it will be only one of several equally plausible possibilities based on the evidence, and it will never ever be anything other than 100% correct in every detail. This will be presented as a natural consequence of Mr. Exposition being very smart, though some audience members might notice when they reach the refrigerator that these "theories" follow about as naturally from the evidence as would deducing the color of someone's eyes from a single shoe print.

Note that this trope does not apply to characters who are able to exposit based on performing actual scientific research (such as Mr. Spock).

Anime and Manga

 * Tetsuo Segawa from Guyver may be the patron saint of Exposition Intuition: thanks to being a science fiction fan, he is able to make numerous, highly specific, and perfectly accurate "guesses" about how the Guyver suit works, the nature of the Zoanoids, that they are being controlled by a major corporation, the various details of the Cronos corporation, the names of individual Zoanoids, and so forth.
 * Ginko in Mushishi almost always seems to know exactly what mushi he's dealing with and how to deal with it.
 * Likewise, Meme Oshino in Bakemonogatari can tell what supernatural phenomena that affected each girl.

Film

 * Doctor Forrester in War of the Worlds. He's able to deduce how the Martian heat ray works, how the war machines levitate, and even determines based on nothing more than seeing what we do that an alien weapon which causes its victims to light up with X-Ray Sparks then fade to nothing works by "cutting across the lines of electromagnetic force" that holds matter together.

Live Action TV

 * Samantha Carter in Stargate SG-1 frequently exhibits this trope early in the series, able to deduce the purpose of alien devices and the nature of various supersciences. As the series progresses, she shifts out of this trope and toward a more realistic "Able to exposit on the basis of training and experience".
 * This is parodied in the episode 200 with absurdly detailed examples of this trope.
 * McKay in Stargate Atlantis often avoids this trope—despite his stated arrogance, he is frequently unwilling to exposit a theory until he has given some piece of technology a thorough examination under laboratory conditions. When circumstances force him to postulate anyway, he's frequently wrong.
 * Daniel Jackson does this just as often, with alien cultures and languages instead of science. He spends most of the episode "The First Ones," with an almost-silent alien that doesn't speak English. So naturally, he spends every scene explaining exactly what he thinks is going on, even when he doesn't have his tape-recorder out.
 * At the beginning of the final episode of the Doctor Who serial The Armageddon Factor, two characters conveniently recap for us some recent events and the predicament the Doctor is in. Which is strange because these events happened on a different planet and no one present has been in communication with them.
 * In a minor example, the kids on Land Of The Lost, who've become fair experts on giant reptilian beasts by this point, are threatened by a two-headed snake in the first episode of season three. Having escaped, they name it "Lu Lu", one "Lu" for each head. How does this fit this trope? It fits, because the two-headed snake's body is completely underwater, out of view, when they run into it. So how did they instantly catch on that it was a multi-headed creature, rather than two big snakes?

Video Games
"Liara: You're a Yahg, a pre-spaceflight species quarantined to your home-world for massacring the Council's first contact teams. This base is older than your planet's discovery, which means you killed the original Shadow Broker sixty years ago, then took over. I'm guessing you were taken from your world by a trophy hunter who wanted a slave...or a pet. How am I doing?"
 * In the Lair of the Shadow Broker DLC for Mass Effect 2, Liara pulls this on the Shadow Broker.