The RPers will explain it better than me, but it works in 2 phases..
1) Decide which order you like to join based on the available Knighthoods from POP 3 that they are portraying in this:
http://forums.taleworlds.com/index.php?topic=189009.0
2) Once you've decided which order you would like to join, you apply to it, (look at that link for examples), and come up with a creative backstory about your character and who he is, etc...
Once that's done, the RP Gods (aka the GMs) will go over your App, and if they like you will accept you in, and naturally give you the link to the other forum where the entire RP process takes place.
In terms of what happens during the RP, well many things, from Story Events that deal with one or all Orders, to a Meta-Game that Mordred has created in which you meet with your fellow Knighthood Orders and lay out plans for expanding your influence in the world of Pendor, from Building Training Grounds, Patrols on your provinces, etc.. (all this naturally caculated in a very detailed spreadsheet by Mordred, since naturally no in-game stuff is required)..
But that's basically the gist of it, and I'm sure in time the RP vets can totally give a more detailed information on it
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MP