Some of the people sitting down to play on Friday night were a bit hesitant at first, but as part of my introduction I said something like this:
"Dungeons & Dragons is a little different from many other games where you sit around a table in that the action happens in two different places. The first place is right here where real people are talking to each other, eating pizza, trying to entertain each other, and having a good time in the process. The other is in a shared imaginative space full of dragons and wizards. In order to begin playing you don't need to know a bunch of fiddly rules (that's mostly my job), instead, you need to imagine yourself as your character and determine how they would respond to their situation.
Anything you can plausibly imagine your character doing, they can do or at least attempt. The rules and dice only come into play when what you want to do is difficult or dangerous or opposed by someone. So as the Dungeon Master, I set the agenda by proposing a scenario for play. You describe what you want your character to do within that scenario. I describe back what happens. Everything else--the rules, the dice, the character sheets--is frosting on the cake."
I could see the lightbulbs going on around the room.
Keep in mind that this speech is a promise that I would go as lightly on the rules as possible and that I would shoulder the burden of managing those rules. She Kills Monsters specifies that everyone is playing a 2nd edition AD&D game, but I wasn't sure of my ability to unflinchingly fulfill that promise with any game other than what passes for BX at my table. So that's what we played.
Additionally, I could've ran any of a bazillion adventures, but I went with the dungeon I've been using for 16 sessions in order to ensure the breeziest play experience possible. I would draw a room on the whiteboard and say, "Now I have to check my notes to see what is in there." But it would only take a glance to refresh my memory then we could get back into the game. I guess what I'm saying is that you want your end of the operation to be as smooth as possible, because you're going to spend a lot of mental energy helping the new players understand the game.
Another thing you need to think about is what materials you give to the players. For some games and some editions, it may be worth the time to create your own truncated character sheet. In Saturday night's game no one needed to know their to-hits, saves, or even their armor class (I asked about their armor and Dex score only after rolling to hit and seeing that I needed to know because the roll was mid-range). I handed each player a ziplock baggie with 3d6, a d20, and one other die (which one varied by bag). I carefully explained what "roll 3d6" meant and that a d20 was the roundest one with triangular faces and the only die with numbers 13-20 on it. You could also use this handout. I didn't have time to print it, though. My printer was giving me hassle and I barely showed up with charsheets.
Finally, I would recommend not using minis or figures the first time you play with new people. Yes, the spectacle of minis is fun. Yes, the tactical display is helpful. But the concept of that shared imaginative space mentioned above is too unfamiliar and too dang crucial to good roleplaying. I generally recommend against anything that can distract from that concept. This goes double for situations like the one Gieljan is in, where his new players are Warhammer fans. They need to see how different D&D is from Warhammer and a definitive way to demonstrate that fact is to play with a big blank space where the terrain and figures should be.