Here is the (paraphrased) RP info from the starter set's dwarven cleric's background:
Alignment: Neutral Good
Background: SoldierTraits: polite, defers to others
Bond: three cousins
Flaw: doubt if the gods care about mortal affairs
The starter set elaborates on the background, saying that you disobeyed an immoral order and got suspended, and now you're out on the road wanting to dish out some violence to folks that ain't got no respect.
I rolled some dice and ended up with Thoradin Dankil, middle aged male dwarf of average height/weight.
After the first encounter (after 3 in-game hours, when I recovered from dropping to zero), I figured I needed to get some inspiration. I checked out my RP info above, and the flaw looked like easy pickings.
It was. I said he went off to the woods to pray, but couldn't get the words out. Just assumed a bitter look and went back to the party.
That's not bad. But, once that inspiration was gone and I was jonesing for another hit, I thought: how can I leverage that flaw again? Just doing the same thing would be lame; it needs to go somewhere.
I could talk about it with another character, but, once you've done that, that's about as far as you can go, isn't it? For instance, I could ask if another player wanted to do a little scene: "How about you ask me to pray for you or a relative or something?" That would give me an opportunity to reveal my flaw. Or I could ask the GM for a scene where I see a leper or something who sees my holy symbol and asks if I can heal him. Both of those would work. Once.
Hopefully the PHB or DMG will have some advice/techniques along these lines; but, until then, I present unto ye:
HOW TO MAKE YOUR STUFF DYNAMIC
In the first instance, show how you are dissatisfied, discontent, or unhappy with some state of affairs.
Example: Thoradin tries to pray but can't.
In the second instance, show the reason for that dissatisfaction.
Example: "A stooped and slender woman approaches Thoradin with her infant son; the kid's barely breathing and is thin and wrinkled like a raisin. She asks me to pray for him. I say, if the gods really cared about what happened to him, they wouldn't have let him be born this way in the first place. She says just pray for him. I do."
In the third instance, you are going to assign yourself a goal.
To do this, you first have to know what you want. What do you want to change? And what significant opposition or situation is stopping you from changing it?
Then, once you know that, what single, concrete achievement do you think will make that possible? Write that down.
Then show your work.
Example: I think: how do I want this to go? What does Thoradin want to change about this situation? Does he want to believe that the gods actually do care? Or does he want to give up all pretense of devotion to the gods to attain some sort of personal authenticity?
Let's say that I want to believe my god is not only powerful but good. Like Mulder, I want to believe.
But I don't know right now how it will turn out; I'm only putting a pin in my destination; I'm not mapping the roads I'll take to get there, not yet anyway; and it's not a sure thing that I'll get there at all or that I'll even be satisfied when I get there.
This isn't plotting a story; it's not railroading or story-before. It's deciding what my story is going to be about—and how I'm going to benefit the party by gaining inspiration like crazy.
So now I know what I want to change: I want to believe that the (good) gods are actually good and do care about human affairs. The signficant opposition is: everything, all the suffering in the world, personal defeats, baddies making saving throws vs my spell DCs, etc. In other words, the opposition is internal; it's my judgments and emotions. It's a conflict essentially about changing my own beliefs. The world itself need not change for my character to overcome or surrender to this opposition.
So what is the single, concrete achievement I think will make this change in my beliefs possible? You don't have to decide this on your own; if you don't know, the other players might have something cool in mind, or the GM might have something prepped that already fits.
Example: I just start making stuff up. Thoradin grew up hearing stories of the Egil Sanguispire, a legendary warrior-ascetic who, because he longed to commune with the same deity that Thoradin worships, dug a pit just wide and tall enough to fully contain his body when kneeling, inscribed the walls with psalms, and filled it with the blood of the god's enemies. When it was full to the brim, he sat in it and breathed until the blood filled his lungs. After ten minutes, he emerged, vomited gallons of blood back into the pit, and the whole thing drained into the earth. He wasn't the same afterward, slew dragons, built empires, etc. They say for those ten minutes he entered the presence of the god and could speak with him as a friend speaks to a friend. That's what Thorin's going to do. He's going to get answers directly.
Single, concrete achievement: build and drown in a pit of sanguispiration.
Now then, I've got to show my work. I'll have Thoradin start digging a pit somewhere and ask the players which one of them wants to come ask me what I'm doing. That will let the explanation enter the fiction. We'll do a montage or something.
In the fourth instance, you've got to advance toward you goal in clearly identifiable steps, suffering setbacks, and really suffering.
Example: digging the pit, killing the god's enemies, collecting and transporting and preserving their blood until I have enough to fill the pit.
In the fifth instance, you need pushback from the world. I'll recruit the GM and other players to pass judgment on what I'm doing and why, to change how I'm thinking.
Example: one of the PCs brings my a drink while I'm in the pit, inscribing runic psalms into the walls. "You know you're just going to drown in there and die, right? It's just a story." How do I react? Another example: an NPC asks me "What are you hoping to learn? What could you gain from all this?" What do I say? Do I even know?
In the sixth instance, I need to change my mind or hold steadfast. After suffering, questioning, exploring the issue through my relationships with the other characters in the game (as above), I need to make a decision: is Thoradin going to go through with his original plan, or has he been dissuaded. Then show your work.
Example: I'm standing above the pit, having filled it to the brim with the big bad's blood, straight from his severed head. Looking very grim. Thoradin has made his decision.
In the seventh instance, show the outcome of your decision. You reach a point of no return; your decision is tested, and you are vindicated or defeated. How you determine this can vary. There can be a whole subsystem implemented; you can ask the GM just to fiat what happens, you can roll for it, take a vote among the players. Whatever.
Example: Thoradin walks away. He fastens the lid over the pit and walks away. However it is determined, it's determined that this will be a positive resolution for Thoradin. Maybe, as a result of everything he's experienced, he can believe in the goodness of the gods without possibly drowning to death in a pit of blood for no reason. Or maybe he ditches his holy symbol and retires or switches his cleric levels for fighter levels.
Alternately, if he had gone through with the sanguispiration, and the resolution was negative, he could just have died, and the party finds him in the morning and holds a funeral, and it's sad. Or he has his vision, gets answers from his god, and they incense him. He emerges from the pit, sets his affairs in order, and kills himself. Or his god blows his mind, and everything is illuminated, even if he can't articulate it to his compadres, and he emerges with pep in his step and a smile on his face.
BUT WHAT IF YOU DIE FIRST?
Sorry, you have a bad ending. Getting a good ending should be hard: you have to survive long enough to get it. If Thoradin dies before his moment of truth, then we probably have our judgment: the gods really don't care. See, Thoradin? You're dead.
WHAT ABOUT SUFFERING?
Part of the drama of the thing is striving after your character's goal, then suffering. The problem is that D&D doesn't model suffering very well right now. If you have hp, you're pretty much fine. If you don't, you're either about to be fine or dead.
So you need (a) some things and people to care about that can be damaged or destroyed in the process to cause you mental/emotional suffering, and/or (b) you need to implement some sort of injury system to model physical suffering. Like every failed death save represents an injury or something.
It could be as simple as: when you fail a death save and survive, you have an injury. GM says what it is, fictionally. Adjudicate any mechanical consequences on the spot.