This is a good question. First a good idea is to look at your favorite novel and see how the author does it. This gets you the basic ‘show don't tell’ stuff for NPC.
However, there is an added difficulty for the story game POV character. This difficulty arises because story games are typically 2nd person narrations, so we never see the POV character from the outside as the story is told through their eyes.
First thing to think about is how narrow you want your narration to be and this depends a lot on the effect you want to achieve. In the dark fantasy business I would always go for a very narrow narrator to achieve deeper immersion. In this case everything they don't see or think about is off the table. Other genre's might not require immersion to the same degree, which allows you to slip in little bits of explanation.
As an author you always want the readers imagination to match your own imagination. But actually this isn't actually nearly as important as authors typically like to believe. Imagine a warrior. You might have imagined somebody with a beard or somebody without a beard, or you may not have thought about beards at all. And all of these things are ok, and also you probably like to convey every detail about your characters to the reader leaving out some of these details can actually make for a more fast-paced story.
Think about your story and try to figure out which part of the details you imagine are actually essential. In particular you want to avoid cognitive dissonance. For example if the POV characters beard has to catch fire at some point of the story, you want to mention the beard early on. If the reader thinks ‘Oh he has a beard, I imagined him differently,’ that's cognitive dissonance, and you want to avoid it.
The only real other reason to mention details is to add flavor and this part of the &slquo;show don't tell.&srquo; We mention the warrior's scars not because they are important to the story, but because we want the reader to know that the warrior is tough, and we can't just tell the reader that we show through the scars.
The next question is when we want to convey the information to the reader. Intuitively one would really like to get everything off our chest right at the start, but this is exactly the wrong approach. Let the action start first, so the reader has something to hold onto. Actually ideally let the POV character score a little win within the first page or so, in this way the reader will start caring about them. How the POV character reacts to some early opposition and success will tell us alot about who they are.
A good rule is the more important a bit of information is for the story, the earlier it needs to go. As gower has frequently pointed out, who characters are psychologically, how they act, how they think, is much more important than looks. Mostly we only care about looks after we are interested in a person, and when looks are described they should symbolize something else. If the POV character bothers to describe somebody's eye color that is a subtle hint that the person in question is a potential love interest etc.
Once the story gets going there are naturally places where you want to slow the pace a bit to create structure. These are good opportunities for some introspection that tells us more about the POV character or his companions.
Now that we have narrowed down the list of things that we actually want to tell and paced them out such they don't come in a big block the question remains how to describe that darn POV character that we only ever see from the inside. A lame trick is to have them look into a mirror at some point. Mirrors conveniently occur naturally in slower parts of the story, e.g. when they come at the end of the first day (where they have scored their first win to make the reader like them).
The mirror trope to introduce appearance is almost too easy. Another way is a different thought of reflection. Want to tell the reader that the character has a beard? At some point he strokes his beard while lost in thought. Want the reader to know he is short? He might recall how he had to cut a bit of his trousers when he bought them. The more important stuff can be shown through their actions. Are they greedy, reckless, thoughtful, aggressive? Then let them act accordingly.
