I've just signed up to this forum to try and offer some guidance in this area.
To become a king, there's several steps you must take. Going on the assumption you're spending the initial portion of the game as a mercenary/vassal of an established King, the MUST DO steps are:
Recruit a party - Ymira, Benduk and the other named recruitables through taverns - this will be the backbone of your new empire and some will make up your initial Lords. I typically assign one or two as "Diplomats" - that is, level them up so there is a high persuasion skill (which, IMO should be a charisma skill, not intelligence, but there we go)
Make friends! Relationships will make the difference as time passes - I'm unsure if it makes much difference BUT if you go the war route, it can't hurt to utilise those relationships to give yourself a few hours breathing room.
Decide whether you're going down the marriage route or not - I understand it's not essential to do so, though you gain some Right to Rule (RtR) from it *I think* as well as the facility to hold feasts (haven't done this yet)
If you're going to rebel against your liege, you must capture a castle or city (Cities (Praven, Velucia, Wercheg, etc.. ) are probably the best to go with economically speaking, castles are usually easier to capture on a troop to troop basis
If you're not going to rebel, and renounce your liege instead, you simply talk to your King and tell him so. You'll lose relationship with him either way. Renouncing your liege and holding properties is a surefire way to start your kingdom off at war with your former colleagues
Also, if you're doing it the "peaceful" way, you'll need to get a negative relationship with another faction BEFORE you can assault one of their cities. Either pick on one of their lords, raid one of their caravans or attack some of their citizens moving between a village and city. You cannot besiege a castle/city until you have a negative relationship with that faction (not the lord, the FACTION)
At this point, whether peacefully or under threat of war, you'll be prompted for a name for your new faction.
This is where your "captains" come in (those named NPCs you recruited from taverns). Start sending them around to promote you as a new legitimate heir to the throne. You'll only be able to send one or two at a time, so plan for this. Also plan for not having your captain for some time as it will take time for them to accomplish their task. With each one, you can get a RtR raise of +3.
Now you need to protect your assets. This is also where your "diplomats" come in to play. Once you've assigned your minister (Partner/Random person/Captain), start sending those with persuasion to other factions to built a rapport with earn some recognition (raises to your RtR).
When recruiting opposing lords, be consistant. Don't tell them what you think they want to hear - they WILL call you on it and that can only be a negative thing.
This is rough and probably full of holes but it should be enough to get you started. The most important this is don't rush it. Bide your time and once you've taken the decision to be independant, stop capturing assets for your current liege - a weakened kingdom is a good starting point to build your own.
Oh, and you can't "delete" a king, nor edit them, as far as I'm aware. If your king isn't assigning you fiefs, check your Controversy (can be found in the "characters" section - easiest way to get it it is to hit "Q" for Quests, then click "Characters" at the bottom) - a high controversy means you're less likely to get offers. While I haven't fully explored this concept, I do think it's greatly tied in to how well you protect your current assets - if your fiefs are being raided and not prospering, this will sky rocket - not a good thing..