In my last post http://www.indie-rpgs.com/forum/index.php?topic=24943.0I mentioned that I was struggling with instructing people how to create and push conflicts. Either I'm explaining it poorly, or I don’t have a grasp on what it is that I do when I play with my regular group. I'm not sure how to approach this topic...

In unWritten there is a Setting Player (like a GM but not) that frames a scene then using elements from the story index.
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The story index is like a character sheet that also has all of the setting details that is used to frame scenes, these things also provide mechanical benefits to the players if they choose to use them. However, the players maybe forced to alter the elements on the story index if they succeed or fail at certain rolls. Additionally, there is a tool on the story index called the story pattern, modeled after the hero's journey that is used to guide the setting player to focus on certain types of conflicts.
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So, based on the story index the setting player pushes conflicts based on the story's premies and the story elements that are present on the story index. once a conflict is dealt with and resolved the players the scene ends and the player to the right of the previous setting player becomes the new setting player.

So, because you only have one conflict before your role as the Setting Player transfers to another player you need to make sure that the conflict counts, that it's pertinent to the story being told, and that it's interesting.

But, I'm struggling to keep people aware of the requirements for what makes an interesting and pertinent conflict. How does one express that? I feel like I have all of the key ingredients, but something just isn't there...

Hi, I haven't read your game (just quickly skimmed over it), but I might be able to give a few hints at how to deal with your question regarding conflict. You might have a lot covered already, but I'll try to address the essentials without being able to interpret what I think you've written in the game text, which I hope will yield a thorough analysis.

According to Lajos Egri, in The art of dramatic writing: its basis in the creative interpretation of human motives (ISBN 0-671-21332-6), conflict can be broken down into multiple aspects.

First, you need to foreshadow it. If it falls out of the blue sky, nobody is going to find it credible. This can be done in a number of ways in RPGs. You might want to front-load conflicts at character creation (Keys in the Shadow of Yesteday), or at least ground them in a Kicker (see Sorcerer). In this way, you can favour play that leads to those conflicts. Dogs in the Vineyard has the GM create a town with problems in it, then the characters show up with their particular traits and relationships... and the alchemy can be quite interesting. Perhaps your Premise does that in the game? It could be a bit vague by itself, but depending on how the characters are created, that could work quite well.
Egri also discusses action and its originating conditions,  and cause and effect. He goes on on how one could pace conflict (not too quick, but it should certainly not be static either). These are probably not very important yet.

The next interesting step probably is point of attack, that is, when to start conflict. One needs to know which characters are involved (and some of their relationships), but especially, one needs to know why a protagonist launches a conflict. It's because there's something at stake and the character can't just sit there.
A lot of games ask players to explicitly state stakes (DitV, TSoY...) before resolving them, others have a more implicit way of doing it (in Polaris you state actions and their result as you go). My Life with Master heavily relies on scene-framing techniques (who is present? what's happening?), and what's at stake is a change of score (depending on the type of scene) that will eventually lead to the endgame.
Is it clear in your play why the characters necessarily have to act in some kind of declination/specialisation of the foreshadowed conflict?

Egri also believes that conflict should show transition. Characters cannot go into a conflict and just stay there (remember when we were kids: "You're a liar!", "I'm not", "You are too", "Not", "Too", etc. we don't want that). Well, at least one character has to move for conflict to resolve. Do your mechanics allow that? A lot of RPGs are not clear on how to deal with "social issues", for example, when one PC wants to convince another of something (often this boils down to pure person to person negotiation/intimidation, power display, etc. "roleplaying", some call it).
DitV has a mechanic where characters gain new traits via fallout from the conflict. A TSoY character can delete a key from his character sheet. As said before, a character in MLwM will have a change in his stats (which are Self-Loathing, Weariness and Love). You might not necessarily need to formalize that though, as long as you get that transition.

To sum it up, Egri talks of crisis, climax, resolution. There has to be a seed for conflict (crisis), somehow a character has to be affected by it (climax) and finally do something about it (resolution).

In RPGs, conflicts are a type of situation born of the union of character and setting. Is it clear to you how character and setting come together to form conflict?
The best thing would be to give a few example from play, where you've seen good conflicts and bad conflicts, then we can check if those elements I just talked about are present or not.

There might be another issue in the way the Setting Player position is passed around and how players can engage with changing their status over play. Examples from actual play are very valuable here. In more classical RPGs, it is clear that the players engage in their characters and that the GM needs to bring meaningful adversity. When these positions change, players might feel awkward at bringing adversity on their PCs' friends (though they might be enticed to do so for some reason).

So, I need examples showing conflicts you've had and how the Setting Player position is handled (why does it rotate at all? what's the benefit of being Setting Player? how do players react to being the Setting Player? etc.)