One good approach is to introduce an already-established character or organization through the viewpoint of an audience surrogate who learns about it along the way. X-Men did that, not just in the movie (with Wolverine and Rogue) but in most of its animated adaptations (with Kitty Pryde in the '80s pilot, Jubilee in the '90s series premiere, and Nightcrawler in the X-Men: Evolution series premiere). Men in Black did that. Doctor Who did that twice -- each of its incarnations, the one that began in '63 and the one that began in '04, started from the perspective of a human character or characters who stumbled upon the Doctor and the TARDIS and learned about them as they went.
Ditto for HELLBOY and even, in a way, Tim Burton's BATMAN, which had Vicki Vale figuring out Batman's origin after the fact.
And WAREHOUSE 13, come to think of it.