You're going to be here for a while and when food supplies run out, that could be disastrous. My biggest tips are to have a ton of food supplies on you before starting a siege and to save before the start of any siege. Archers will use them as cover while firing at guards above.
Here is the full list of siege weapons you can develop during the siege. If you are the defending player, this means you can construct plenty of siege weapons to counter their efforts to take over your settlement. It's worth noting that the enemy factions can do the same to towns and castles you own as well. The speed at which you construct your siege camp and any siege weapons is based on your Engineering skill point total. This gives the defending forces a chance to build up their defences. You'll then begin the long process to constructing your siege camp, which must be done before developing any siege weapons. When you approach a settlement owned by an enemy faction that you are at war with, you will get the option to lay siege to that town.
How to siege a town or castle in Bannerlord