I'm thinking about a whole complex of problems, and about buymeaclue's frequent and absolutely correct assertion that the correct answer to any question on writing is 'it depends.'
And the fact that many writers (not all) follow a course in their development where, at first, we tell too much. We explain and exposit everything. And then we get told 'show don't tell' and 'exposition is the very devil' and we stop explaining.
And become incomprehensible.
(There's an associated complex of problems that is writer coyness--inexperienced writers who think the appropriate way to tell a story is to conceal as much from the reader as possible, and then either reveal it in a twist ending, or leave it to the reader to figure out what the story is about. Often, I think, this second issue is because the writer doesn't actually know what the story is about, and is hoping the reader will make something up.)
In any case, I'm going to go on record as saying that, in my opinion, exposition is an art. And good exposition is so integral to the structure of story as to be almost indispensable. There are writers who can get away with a story that is almost all expo, and there are writers who can tell a story almost entirely without it, but we mere mortals in the trenches must compromise.)
And in side notes, today in Neil Gaiman's Blog we get this article of discussion:
Well, you're writing to communicate. Unless part of what's important about the story is that the reader not understand something, if you're using a word or term that you know most people reading won't understand, then explaining it somewhere, somehow, not necessarily the first time you use it, is a wise idea.
As for how you do it, that's your call. If you do it with enough assurance, you can simply tell people things. Or you can have your characters tell people things. Or you can footnote. Or have a dancing paperclip leap in and explain, then fly out of the story never again to be seen. As you say, do what you think best: that's the joy of being a writer. You get to make your own rules and build your own worlds, and things happen the way you want, because you say so.
Go there and read for more.
Also for your delectation: Charles Coleman Finlay on The Artful Infodump.
Moderation in all things. Including moderation.
(papersky's concept of 'incluing' and my own beloved 'infobolus' would also come in for discussion here, in a rational world, but I'm working on a short story. Which has a lot of exposition in it, come to think of it.)