To help other GMs do this, I can certainly write out some instructions and advice. "Here's what you must do. Here are some tips on how to make it easiest on yourself, and get the best results."
However, I'd rather give GMs an interactive game bit. Something immediate and easy to use. A few nights ago, I came up with this:
The F T Meter
In addition to defining your NPC's Need, and the Reward they'll give the PCs if that Need is met, also rate the NPC/Need's Transparency and Flexibility.
Flexibility: how difficult it is to get the Reward by doing something for the NPC other than satisfying their Need.
Transparency: how difficult it is to get the NPC to tell you what their Need is.
Assigning these ratings should include fleshing out your concept of why the NPC isn't simply cooperating. For example, here's a paranoid opportunist:
The positive check in F means this NPC starts off fairly open to incentives other than money. The two negative checks in T mean this NPC does not want to reveal that they're motivated by greed.
How to use this in play:
The GM doesn't let the players see the meter. Each time a player character speaks to the NPC, the GM goes with their gut on how the NPC would react to that, then quickly checks off whichever box is most appropriate. There are four options. The NPC is either:
a) buying the PCs' arguments and accepting whatever the PCs offer
b) trusting the PCs more and getting closer to revealing their Need
c) giving up on getting their Need or anything else out of this
d) giving up on feeling safe enough to reveal their Need
The GM then roleplays the NPC's response, incorporating the box they just checked off.
1) GM thinks, "Oh, the NPC would like that!"
2) GM checks off a positive F box.
3) GM says, as NPC, "Ooh, very nice. Well, yes, I may have some interest in that..."
In this example, there are still positive F boxes unchecked, so the conflict isn't over; the PCs could still screw it up. But they're probably in good shape if they can find any sort of decent way to continue from the last thing they said.
It's through this back and forth that the players investigate the NPC, testing out different approaches, seeing what is and isn't working, and revising their strategy accordingly.
The conflict ends when any segment of 4 boxes have all been checked off. If it's a set of negative boxes (frowny face), the NPC is unwilling to continue the conversation. If it's a set of positive boxes, the NPC gives the PCs their Reward.
Here's how the paranoid opportunist encounter could play out:
This NPC got nervous over the PCs' do-gooder appearance, then responded well to their offers of sharing the fruits of their adventure, then disliked their specific offer to introduce him to the powerful friends they'd make, then went for their promise of loot, then bought in whole-heartedly when they speculated on what sort of loot they might find.
The GM roleplayed each of these reactions, the players paid attention and came up with some clever responses, and they achieved the Reward: the NPC tells them where the secret door is, and now they can enter the underground complex.
Note: every obstacle in Delve could be conceived of this way. A dungeon room has its way out, and it's level of difficulty in finding that way out, and it's level of flexibility on improvised other ways out.