You can choose to let a siege run its course until the defenders are wiped out by starvation, but it’ll also cost you a lot of time and food. Likewise, you can choose to play a siege battle manually by leading an assault, and you’ll be able to use the siege weapons you’ve built. For instance, the trebuchet can be aimed at a general direction (W and S keys), but you can’t control how high or low (or how distant) it’ll fire. Alternatively, you can send your troops which will auto-resolve the siege.