To quote the wiki:
Castles are found all over Calradia, and each one has a nearby village. In order to take control of a castle, you must besiege it...
With an enemy castle...you have the option to besiege it and claim it for your own...
There are other ways for a faction to capture a castle in Warband other than just besieging it. They can also wait for the food supply of the castle/town to run out, and then take control, or if a lord holding a castle/town defects without being indicted, it will go to the new faction defected to...
Should the player conquer a castle without being sworn to a liege, he takes the castle for himself, and founds a new kingdom...
If the player conquers a castle when they already have their own new kingdom, they are given a list of Vassals that are with the player's kingdom to take control of the castle, the option for the player to take control of it is available, and the option for the castle to have no Lord is available as well.
So, you can either revolt against your current kingdom to found your own and conquer a castle for yourself through one of the methods mentioned (or conquer and then possibly decide to revolt if the king doesn't give it to you) or become buds with your king and convince them to appoint you as lord of a castle.
If you conquer a castle yourself, like when conquering a village or fief, you can ask your king to give it to you and if they don't you can either renounce your oath and fiefs, renounce your oath alone and take your fiefs and the one you just captured thus causing you to rebel, or you can take a payout. The kings apparently make the decision randomly, but key factors seem to be renown and relationship with the king although there is some mention that each fief, city and castle holds some value and that kings try to balance this value out across all vassals. Apparently you can possibly convince other lords to support your claim to the castle with some persuasion.
