How does one take land when they are not in a faction, and then make their own faction?
You can revolt in a few ways AFAIK:
If you lead the siege on a city or castle (that is, you're the one who started it) you can ask for it to be given to you. The siege leaders get a hefty weight bonus when determining who gets it, so you'll likely be the one. If you don't, though, you can choose to break off as a rebel faction and you'll take that place and all other castles and towns you own and automatically go to war with your parent faction. An easy way to get this is to accept every stuffty village you're offered, since the odds of you getting a fief decrease the more you have already.
You can also side with a claimant and start the endless war against the main faction, although this only lasts until the rebel faction wins, then the rebel faction becomes the "main" faction again. This is mostly used to get rid of annoying rulers, like King Ragnar of the Nords. For some reason, Ragnar loves giving himself tons of fiefs. His claimant doesn't display this behavior, so it might be worth it to make him the new King.
The last way is to simply attack a town or castle as an independent person, I.E. not a vassal of anyone. This is hard because garrisons are hundreds strong and you have no allies, just what you bring to the fight. Also, if you don't have enough right to rule then you might end up with other rulers not taking you seriously if you do manage to capture the place.
