Codify what you and your players know.
Anything which the lot of you agree is there is there.
That's actually quite a bit harder than it may seem. Often, some data is well known - species, classes, cultures, weapons, maps - but lots of other data isn't presented in game nor in the hint books. Both Final Fantasy and Zelda lines are notorious for hiding lots of information in the dialogues, and more in the pre-release adverts, and more still in the in-box documentation, and then releasing tidbits through the hint-books.
Pick and choose, and define what canon resources are "valid" for your game.
And, in the case of videogames, discuss the feel and themes, and work with the players to make the tabletop rules address the thematic and tone issues. Make notes on what the players expect, and what they don't mind you changing.
Even in cases where you're playing an RPG with its own canon - if you as a GM don't have access to some bits, tell the players ahead of time, and don't hesitate to say, "And if I don't own it, it doesn't exist for the purposes of this campaign." (The mixed blessing of this is that, if a player is strongly enough enamored with Splatbook Xyzzy, you may wind up with a copy anyway... even tho' you didn't buy it because the reviews said it's totally broken....)
Define where you're going to play.
If the map ends on the oceans, or the fiery fields, or the "edge of the world cliffs," you may need to work from the extant maps.
The extant maps are no different than for any other semi-mapped world. Expand only what you have to, and only when you need to.
The problem is that the other supporting details won't be there. Be prepared to Make Stuff Up.
Define when you're going to play.
Most computer games have some major change in the timeline happen in the game. Often, it's due to the main plot the player engages.
Changing the timeframe can make tabletop easier.
Setting a good bit before the videogame means that most of the setting information is going to stand up, but a little can be changed, and players have little recourse to "but the Nintendo Power Article says..." If you're far enough back, say, a whole generation, most of the NPC's won't be of importance, either.
Setting it right after the ending is great - unless, of course, they're working on a sequel. You can find the surviving big-bad-guys and major-good-guys in the walkthroughs that are almost too common on the nets....
Declare a separate continuity.
Once the game begins, it's generally a good idea to bar the addition of any new source material, unless you as the GM add it.
Also, if there is potential to overlap the game's timeline, just state ahead of time that the timeline isn't fixed in stone, and may change due to any combination of Player Actions, GM brain-cramp, and GM encountered/acquired materials.
Have a clear vision as a GM.
The others in the group don't need a clear vision. You do, mister GM. You need to see in your mind that setting as being at least as alive as, oh, say, a major motion picture you just saw.
That view doesn't need to be complete, doesn't need to be right, doesn't need to even be shared with the players... but you'll draw on it every time you build adventures and NPC's.
Pick a ruleset that you know and that fits the setting.
D&D isn't great for doing EVN, can do Fallout passably, but is the very system behind Pool of Radiance. Certain flavors may even work for Bards Tale.
GURPS will do Halo or Star Trek Elite Forces just fine, but isn't so hot for any of the Zelda games - D&D even isn't that good a fit - but Fate Accelerated can very readily do it quite well by retheming the approaches to Melee, Missile, Magic, Social, Music.
Picking the right game system means not having to write many pages of cumbersome adaptations. Still, during the d20 heyday, not a few such books wound up in print, and some were actually decent!
Knowing the ruleset well allows knowing better what you need to tweak. It also allows knowing whether or not the game's a good fit in the first place.
So, taking, as example, Ambrosia Software's Escape Velocity Nova...
Were I to run it, my players wouldn't actually know the setting. At least at start. One might buy the game just to see what I'm pulling.
There's a lot of buried information that I've just not been able to play through. (I've poked through the files, using ResEdit, and wow - I've only hit about 10%, including the one time I finished the game! If you finish certain of the storylines, you utterly change the setting. And you can't avoid the major themes, tho' you might not recognize them, and might not trigger the plot line, but you WILL encounter it, and it will wait for you to trigger it.
So, knowing what I know, I'd just use the maps, major governments, and basic ship types. I'd pick one of several games, depending on player base.
I'd also use the starting condition. I would probably have the Vell-Os plotline in the background, and the Aurora-Federation War. And from that point on, everything else is just reactions to the players.
Now, looking at what games I'd pick...
- It needs to support blasters of some kind.
- It needs to support spaceships fighting.
- It needs to have psionics rules.
- It needs to have rules for adjusting prices on trade goods
- It should require few houserules.
- It doesn't need non-human PC's, but can use different racial mods for the various sub-races of humans in the setting.
Potentials: Traveller, Diaspora, Serenity, Buffy the Vampire Slayer, Edge of the Empire, Firefly.
Traveller: Blasters need to be houseruled. The Vell-Os ships are houserule, and the acquisition of Psi is also in need of houserules, because all Vell-Os are both telepaths and Telekinetics.
Diaspora: Blasters need to be defined. Ship combat and travel is very workably close, but the maps replace the cluster maps system. Size matters in the EVN setting, so that needs to be adjusted to be covered by ship creation. Psionics are underdeveloped, so that's houserule time, too. Reject, unless my players are FATE Junkies.
Serenity: Needs blasters. Needs jump drives. Otherwise, it's got room for everything but the Vell-Os, and the Vell-Os can be adapted from the Psionics rules. Given the looseness of the system, adding blasters is trivial, and the Vell-Os ship-making is easily added as a series of skill level driven gains. Ship combat is pretty minimalistic - the eponymous ship is unarmed.
BTVS: Yes, I'm serious. Angel, or Army of Darkness will work just as well. There's an adaptation in Eden Studios Presents vol. 1, called Spacefarers and Prariefolk, obviously intended for being Firefly sans the license. So... It needs some trade rules help. But it does have a hand blaster. And it has a great magic system, from which I can fake up the psionics rules. Be a lot of work. But the feel of the game itself is very much fast paced, player involved.
Edge of the Empire: Blasters? Yep. Flexible rules? Yep. Ships? Yep. Space Combat? Oh, yeah! Psi? Yup - adding the vell-os ships is pretty straightforward. Size does matter. Lots of room for modifications. Problem: iconic game books.
Firefly: (Note: NOT the same game as serenity, despite the same publisher!) Blasters? no problem. Psi? Yes, but limited RAW. Ships? Yes, and very flexible, but not covering cargo. Trade Good rules? Not in RAW. (Yeah, surprise! Trade is a MacGuffin in the Firefly RPG.)
So, in the final decision, Traveller or Edge would be my first choices, then Buffy, then Serenity. Firefly would need some major work...