I've been running an X-Files style game for a few years now using the Conspiracy-X game system with a home-brewed setting.
Methods for getting players engaged in the world behind the curtain is in many ways dependent on players' nature and general type of system chosen. In my case, I've chosen a less Nar game engine and am running the campaign as an evolving sandbox. The techniques I'd employ in something like Fate would vary a fair bit, but the basic advice would be the same.
Stress to the players that this is an investigation/exploration game rather than a monster-of-the-week style that has similar trappings.
Some basic tips:
Begin as you mean to continue, just more obviously. The first scenario should have at least one and possibly a small number of things the players can dive beneath. Consequences for failing to dig should be blinding obvious in retrospect to the players, but not be especially annoying. Trigger points and chain reactions should be simple to work out from the end situation so the players can begin to correlate the potential engagement point with the result of engagement/non-engagement.
Keep the number of attack points reasonable and reasonably obvious that there is something odd to potentially engage with. In D&D, if every door could be a trap, the game bogs down as the group tries to mitigate the danger at every doorway. Similarly, if anything could be a clue, the game either bogs down as the group tries to investigate everything or the players give up trying. The very occasional red herring is OK, but I let the players introduce those themselves and don't include deliberately misleading information.
Be prepared for the players to miss opportunities you find glaringly obvious. Be prepared for players to assemble clues into shapes you wouldn't think possible.
Keep the number of factions and splinter groups reasonably small. The players have a small window for game information. For the same reason, keep motivations simple. Recurring characters/factions can develop nuance and depth over time as the players peel the onion.
Give the different factions common signatures – things the players can pick up on after several encounters so that they can prepare when they detect the same pattern next time.
Make certain that digging into the background offers material benefit. New ways to combat the darkness, circumstantial allies, additional resources, and/or enhanced survival techniques help inspire the effort. Discovering trivia for the sake of trivia can motivate some player types, but not all. Digging into some of the background should make the current situation easier to deal with.
Digging should be trap-free in general with the only cost being the time invested. If the side investigations are seen as inherently dangerous they will be dropped. If there is risk for digging deeper, make the stakes known to the player upfront as part of a pre-discovery discovery.
