I think there are two basic solutions for exposition, and fortunately they're not mutually exclusive.
The first is to minimize and streamline it, by choosing your background info carefully and then distributing that information alongside other interesting things, like say the billboards your character zips past during a hovercar chase scene. It's a method that's usually credited to Robert A. Heinlein, and which Jo Walton gives the neat term "incluing."
The second is the old-fashioned method -- make the pure exposition itself as interesting as possible. Learn the rhetorical tricks of good nonfiction writers and lecturers, and make your infodumps fun.
I think Neal Stephenson's Snow Crash is worth studying for great examples of both techniques. Snow Crash has both a dizzying opening that sets the stage for the whole future milieu, and a long section deeper in explaining the major science fictional idea of the story.
Many people say they hated the long explanation, but personally I enjoyed it at least as much as the opening. Then again, I'm a weirdo who sometimes skips ahead to the next infodump. But I figure there must be at least a few other readers like me.
Another trick you can pull with the long lecture-y explanation is to add stress around the edges -- the guy lecturing your hero is doing so while waving a weapon, the lowdown on the conspiracy is delivered under a dark bridge or a spooky underground parking lot, or there are ominous bumps and scratches outside as the lecturer speaks about zombies... A great example of a long infodump with tension is "The Shadow of the Past," Chapter 2 of The Fellowship of the Ring. Check out Kate Nepveu's commentary here, and consider what a great history professor Gandalf would have made.