I haven't run a ton of RPGs, but all the ones I have run had the advantage of gathering the players in one central physical location. That allowed for at least a quick verbal run down of the rules before the game started so everyone had an idea of how to play. Since we won't have that luxury I thought I'd write up just a quick set of the basics. I still recommend reading the character building section of the book so you can pick an archetype that appeals to you, but don't worry too much about game mechanics. If all goes according to plan you should just be able to describe what you want to do and I'll tell you what you need to roll in order to succeed.
For Dark Heresy you only need two 10 sided dice per person for the whole game. If are unfamiliar with oddly shaped dice but have a typical D&D dice set there should be 2 10 sided dice in it, one numbered 1-0 and one that goes up by tens, 10, 20, 30 etc. So if you were to roll a 20 and a 5 you would have a total of 25, 70 and 2 would be 72, and so on and so on. If you don't have a die that goes up by 10's just pick one die to be the 10s place and one for the 1s place (it helps if they are different colors).
Every test in Dark Heresy will be made like this, and the goal is to roll low. So if you are trying to lift something heavy over your head and you have a strength of 40, you would need to roll 40 or lower in order to succeed. They more difficult the task you are trying to accomplish the more difficult the test will be. Something heavy like a refrigerator would something like a -30 modifier where an oreo cookie would have a +30, so to lift the fridge you would have to roll under 10 and to lift the cookie you would have to roll under 70.
Of course those are silly examples and lifting a cookie would not really require a test, but you get the idea.
Degrees of Success/failure
Another important concept is degrees of success and failure when testing. for every 10 points you exceed your goal you get an extra degree of success. When shooting rapid fire weapons you get an extra hit for every degree of success, when interrogating a subject the more degrees of success you get the more information he will divulge. So if you were firing a rapid fire (+20) lasgun at a target at point blank range (+30) and you have a ballistics skill of 36 and rolled a 56 you would succeed with 3 degrees of success hitting your target a total of 4 times.
Hit locations and armor values
For determining damage things get... a little weird. first you flip the number you rolled (so the 56 becomes a 65) and then compare that to the hit chart which shows where on the targets body you hit. Don't worry too much about that part, again I'll do that for you. So just for an example lets say you hit the bastard straight in the head, cool right? Wrong! He was wearing a badass helmet and nothing else because...because...I can't think of any reason for him to do that, but who can fathom the followers of chaos! So if your gun does 1D10+2 damage and you rolled a 5 (equaling 7 because math), but he is wearing a helmet with an armor value of 4, you are already down to only 3 damage getting through the helmet.
Toughness Bonus
Is that enough to get through his thick skull though? All players and NPCs get to subtract their toughness bonus from any damage they would take as well. Your bonus is whatever the 10s digit in that characteristic is. So if you were a little weakling with 21 toughness your toughness bonus would be 2, if you were a hulking feral warrior lord with a toughness of 46 then your toughness bonus would be 4. So as long as the naked guy in the helmet has a toughness of 29 or less your shot would at least injure him, anymore than that and the combination of his helmet and thick skull protect him entirely.
Critical Damage
Combat will happen at times, but should be avoided if possible as you are not superhumans and are quite fragile and easy to kill. If you get injured enough to go below 0 wounds you don't automatically die, but every time you take damage that puts you further in the negative you have to roll on the critical hit table. Sure you might get lucky and just get stunned, but there is also the chance that you will roll the result that has your head pop clean off and your body continue running around spraying your teammates in blood forcing them all to take fear tests or start going insane.
Surviving the unsurvivable
While your characters are not superman and thus can be killed just as easily as any other human being, they have been picked out by higher powers for a purpose. What that purpose is may not be known, but generally someone out there wants you to stay alive long enough to accomplish something. To represent this you have fate points. Everyone starts out with a number of fate points and they refresh at the beginning of every game session. You can use them to re-roll missed hits, cure yourself of some wounds, recover from stun effects, and various other useful things. In more dire situations you can "burn" a fate point. This means that the point will be destroyed and your pool will refresh to one less each session now but this can be used to survive something absolutely ridiculous such as being launched into the vacuum of space or shot in the face by a tank. Surviving doesn't mean that you will come through it all okay though, you are still going to have some horrific injuries or missing limbs and those affects will be permanent (although in the future augmetic limbs are easy to come by). Rule of thumb, don't get shot by tanks or launched into the vacuum of space, but if you do all is not lost. Just most is lost.
Insanity!
You are going to witness some scary or horrible things and when you do you will gain insanity points. Get too many of these and you will start to develop permanent mental illnesses. If you get 100 insanity points your mind fractures and your character ceases to function. At this point the character is effectively dead. Don't worry too much about insanity killing your character though because the more insane you get the less scared you get of things so the less likely you are to go more insane. Insanity points can be removed but it is usually at a high cost.
Corruption
Corruption is similar to insanity in that if you get 100 points of it your character will no longer be playable. This time though it's not because your head pops off, or you got so scared of the gibbering creatures in your head that you become catatonic, no this time it's because you are on your way to daemonhood. You are no longer one of the "good guys" and now are exactly the kind of thing that your little band of adventurers is trying to kill. Corruptions can be gained by doing foul deeds, or just being too close to the raw energy of the warp. Corruption points are permanent and there is no way to remove them.
I didn't proof read ANY of this so sorry for the probably trillions of mistakes and nonsensicalities
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