A siege is a long, slow
battle accomplished less by
conventional warfare than by
starvation,
dehydration and
biological weapons.
Here's how it works. Say you want to attack a city that's well-defended, and you know you probably can't force your way in. You do have enough troops to control the traffic to and from the city, however, so you place an embargo on everything. Food, water, supplies, you name it, they'll eventually run out of it. Poisoning the water supply will speed things up, but be sure to find a clean source for your own troops.
While you wait for the residents of the city to surrender, you can take your sweet time in attacking. Dig tunnels toward the city walls and perhaps you can get enough explosives under the wall to create a breach. You can also use a catapult to hurl things at the city. Impact projectiles (rocks, for example) are traditional, but you can also throw in disgusting stuff like carrion and feces. This will make the residents hurl, and perhaps give them a disease problem.
If they haven't given up yet, try your luck with other siege weaponry like a rolling tower to get your troops into the city. Remember that most of the people they kill will be grunts; the important people will often have locked themselves in a stronghold with supplies. You may then have a second siege on your hands.
Sometimes the best way to end a siege is to offer generous terms of surrender -- all civilians to be spared, all soldiers to be disarmed, and only the officers to be hacked to pieces.