There are different ways to do it. The easiest way (in my opinion) is to capture as many castles/cities (preferably the latter) and ask the king to award them to you. Some day, he won't do it anymore and you can keep all those fiefs for yourself while breaking free. Huzzah!
The faster way would be to support the claimant of Vaegir (Valedym the Bastard Prince as far as I recall) and then tell him that you can't help him anymore with the rebellion, so you are the "king" of the rebel faction. Mind you, this only works when you have a castle/city already and you will loose a lot of honor.
I think if you play as female, you can also ask your husband to start a rebellion, but I never tried that. Seems interesting though...