How do you take over a castle?

There are many ways: Spies could infiltrate it, opening the gates for your army to enter. You could blast or catapult rocks into the walls until they fall down, allowing your army to get inside. The cheapest way is to get regiments of infantry with ladders to climb up one of the walls and capture a tower, giving them a foothold. Besieging the said castle works also. If no food or other supplies pass into the settlement they will eventually starve and surrender. It would also be possible to undermine the walls. This means digging under the wall and setting fire to the supporting timbers, causing the walls to topple.