I'd be interested in your ideas how to achieve that in a video game. It'd definitely feel more immersive to actually teach rather than just have a few mumbled lines while sitting and then "ding" instant Jedi, but how?
Maybe after a few battles you'd get an oppurtunity to 'teach' them a new skill, or something, and after so many, they'd become full Jedi? I dunno...I'm not an idea-person...which is why I'm asking you what yours are.
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Well, at first they would just level up in the "Force Sensitive" class, they would pipe in every now and then about what the party should be doing, and you tell him/her what you think of their opinion and why. After you've guided them for a good 4 or 5 levels, they become a jedi class based on what you've been teaching them. If you've been emphasizing action, then they become a guardian etc. Have them only able to learn force powers that you already have until they reach full jedi status. Realistically any apprentice you take in the game wouldn't reach full jedi status at all, but its just a game.
Maybe have a choice of apprentices, and those apprentices will take your teachings a different way. Like one will be resistant and headstrong and more likely to turn to the dark side, while one is humble and more likely to go to the light.