Here's the trick: Each point of Karma you wager must come with a bit of narration that advances the scene. Most of the time, these will be stunts (combat moves, cinematic flourishes, etc). Witty lines of dialogue, clever metaphors, and flowery prose are also fair game. The same system works for investigation montages, interrogation scenes, and so forth. Of course, you should avoid negating anything someone else has already described. It's just good improv.
Character Descriptions: Karmic characters have no stats; they're described in purely narrative terms. Just put together a paragraph or two that outlines their background, personality, skill sets, etc. (In the SW games, all the Jedi will be assumed to have Force powers, lightsaber training, and some investigation skills.) You'll suffer no penalties when using skills that aren't mentioned in your Character Description, but the narration that accompanies your Karma Points should involve succeeding through luck, rather than skill.
You should also come up with a few Flaws. You can earn Karma by role-playing your Flaws, as long as it gets your character into trouble. Of course, you can earn Karma by doing anything that gets you into trouble (as long as it's entertaining trouble); Flaws are just a handy source of inspiration. (For the SW game, try to have at least one Flaw that can be used to tempt you towards the Dark Side. I love doing that!)