Any question you can use to connect two players in any way is good. Start off slow: "Who brings you gas? Who works on your car? Where do you keep it?" Start off with facts, then move into opinions: "Who would you let ride your car? Do you like giving him a ride, or her?" etc.
Pretty much as you said, ask things, and when they give you an answer, ask questions about that answer. You're on the right track if you're asking three or four questions in a row. Pretend to be a journalist, covering articles for Apocalypse Weekly.
Now, a standard set of questions you should ask is difficult, because it all depends on what the players are playing, who the characters are, what the setting is like, etc. So these are kind of general, and you fill in the details yourself. But:
- Try to get a few conflicts going. Don't force it, but get people thinking. Start with the small stuff: think about the people you know, your actual friends, and model it on that. "Do you like hanging out with Jag? What's best about crashing at Fido's place?" You're looking for opinions, trying to cultivate them, because that's what conflict is in Apocalypse World. (It's not like D&D, for example, where the conflict is, "the evil wizard is kidnapping maidens! We must bring glory to the forces of good!") Conflict in Apocalypse World is hardcore social. Conflict here is, "That motherfucker stole a gun from me when he stayed here the other night!" - "Dusk has been talking shit about me, let's go settle this."
Apocalypse World is a lot like reality television. But imagine it as really unscripted, not just pretend unscripted. Just an honest documentary on limitless people in limitless situations.
That's why it's so important to really zoom in on them in the first session, A Day In The Life style, to learn what's what.
So find out who thinks what of whom, but also start to promote this line of thinking: what do you think of her? How do you behave around him? Then when you sense the slightest bit of friction: "You prefer staying with Vision? Why? What's wrong with Absinthe?" Remember, you're not making enemies - just friends with opinions of each other. I like my room-mate, for example, but he can be really passive aggressive and that's annoying. That sort of thing. Conflict.
- Find out three things: how people get around, where they make money, and where they get supplies. What's important to us, as people? Getting rides places, having correct bus fare, not running out of gas. Keeping our job, paying rent, getting groceries in. Paying bills. Same in Apocalypse World, but with a different face. Isn't it neat how this game is just everyday drama, it's our real lives, but the simple fact that society has collapsed makes shit dangerous all of a sudden. It's like living in a bad neighborhood: talking shit about someone means they're going to find you and hurt you.
- It's optional, but a lot of fun, to make a love triangle, or at least a relationship. Don't force this, but definitely nurture it when you see it.
- Find out what's making life difficult. There's something out there, above and beyond, that's making everything less than cozy. Is it the radiation storms that can kill you? Gnarly, the warlord, demanding money and blood? The crumbling infrastructure of the hospital we all stay in? It doesn't need to be a time clock or anything, but something to put stress on the characters.
And really, just go from there.