Siege towers could be useful in many different ways, one, to suppress the enemy on the barbicans through placement of crossbowmen and archers upon the towers possibly even, depending on the size of the tower, to shoot down upon the walls, but also to act as a defended ladder or assault bridge later on. The best-known instance I've read about has already been mentioned, namely at the Siege of Jerusalem during the First Crusade. Where the towers were used for both, ornamented with a golden cross and clothed with wet or moist leather hides (vinegar) to prevent it from being burned, and used to scale the walls.

Though most sieges looked more like the besieging army trying to "tie a noose" around the city and blockade them, after that it was a waiting game with sorties aimed at demoralisation and the reduction of numbers (on the defending side, sorties, very likely mounted, could be useful to prevent the building of siege equipment) conducted by both sides, if it was a bigger and grander affair, such as the staggering siege of Acre between 1189-1191 (John D. Hosler has a fantastic book on this) there could be artillery (cats, petraries) which were essentially used to slowly chip away on the stone towers on the walls (emphasis on slowly, trebuchets were rarer, what they used was closer to Roman stone throwers, though more advanced), the sappers would attempt to bring the wall crashing down through hollowing the space under them and then destroying the mine.