Game is pretty difficult but you should practice sieges as a vassal or mercenary first.
Level up stewardship, get a family member or companion with high steward skill in your party or get a higher clan tier or get more perks to have more party members.
If you want to siege a building you should try to aim for at least 200 high tier archers with a good captain preferably fian champions because you don't have to spend much time sieging just set up the base camp and if you win the ranged war you basically neutralized their siege advantages because you can snipe them before they can use their siege weapons and snipe them off the walls
Most of the time sieging ends up in 5 ways
Ranged option (recommended)
1.) You attack immediately, you will have zero siege equipment (unless you have some engineer perks) and they will have their walls and equipment. The only way you can do this with a small party is you have a lot of great archers for suppressive fire a party of almost all archers, you could sneak up a ladder and open the doors but honestly that is pretty risky to do and they could just shut the down and even with a strong character if they have high tier crossbowman they can kill your character pretty quickly.
2.) You build some siege equipment like a ram or mobile ladder. This way works if they don't have catapults (otherwise they will break your siege equipment) if they don't you will lose some people this is probably the least recommended option it is basically to save time if you have a bigger army you don't have enough people pre-kingdom to do this type of siege.
Melee option
3.) You build 1 ram then onagers/trebuchets and disable their defenses. This works good if you have high tier infantry with shields, without siege equipment they will just have archers but you have shields and you push the ram to the door and fight them off. This takes a lot of time though and don't have a lot of time unless you are sieging an obscure location against a faction with its vassals imprisoned or tied up
(recommended for rebel kingdom)
Destroying the walls
4.) This siege you just break down the walls, this one takes way too long for a new kingdom unless it is a rebel faction but if you find a very good fief that has rebelled you can do this option and you don't even need a big army after you break the wall a bunch of soldiers will gather to fill the breach and you can easily get a lot of them with siege equipment and level up engineering as well
5.) Sieging a recently sieged fief, a fief like this will usually be empty so as long as the coast is clear you can sweep fast a recently sieged fief and take it over even with a mediocre party and no siege equipment.
The easiest way to start a kingdom is to become a powerful vassal and break off.
I disagree with the sue for peace, real strat says to do that but the problem is that you will pay way too much in tribute and you and any vassals you have will go bankrupt. You should never ever pay tribute if you want to be a sovereign kingdom, if you are having problems with rogue vassals from a destroyed kingdom you should either execute them all, keep them in prison or recruit them to your kingdom, if you can't defend your land it means you do not have enough vassals.. You have to just assume you are going to war with the whole map and many times a kingdom will declare war on you but never do anything so you don't need to have peace with them.
What is better to do is let their army attack your castle have one poorly defend fief to function as a magnet and then farm a bunch of influence to get your policies that you want and then just start mass producing vassals, it does not matter if they lose their land at least for the first few years, just get as many vassals as possible ASAP it makes a huge difference and you need a lot of vassals to take over the whole map.