When you move from the open battlefield to siege warfare, be prepared to shift your whole attitude. Whereas conventional battles tend to be resolved rather quickly, sieges will take several seasons to conclude, successfully or not. Whether you're planning to storm a castle or defend one, you must plan siege operations carefully and methodically.
True, most sieges climax with a desperate melee inside the castle walls, but you'll usually spend much more time trying to breach those walls or prevent the enemy from doing so. Archers really come into their own during sieges, so you may want to reorganize your army a season or two in advance of a siege, so that you'll have more of them.
Before you can hope to storm a castle, you must thin out the ranks of the defenders. Only massed arrow fire or catapults can do that. If you attempt to wheel up your siege towers and battering rams before you've weakened the garrison, chances are that the crews will be slaughtered and the siege will fail.
If you're defending a castle, be very careful about when and where you deploy your vats of boiling oil. Remember that you only get a certain number of these per castle, and once they're used up, your ability to repulse an assault diminishes greatly. Watch out for feints by the attacker and try to save the oil for use against towers and battering rams -- its effect can be spectacular, if not decisive.
And finally, a word about guerrilla tactics. If you are not yet strong enough to engage in a full-strength campaign against a more powerful neighbor, simply march an army cross-country and on to a square containing a mine, quarry, sawmill or forge and that facility will turn to a pile of blackened cinders, with serious consequences to your enemy's economy. Of course, this only works if you can hurriedly withdraw your force before the enemy can intercept it.
It's also a double-edged tactic. If you conduct such raids into a province you plan to occupy soon, you'll also be damaging your own economy, since those ruined facilities cannot be made operational again without many seasons of effort being devoted to rebuilding them.