A common mistake that people make when photographing fireworks is using a fast shutter speed so that they can hand-hold the camera. The problem with this approach is that the fast shutter speed freezes the action of the fireworks blast. The long trails that are the hallmark of good fireworks photography come from using a slow shutter speed. If you don't understand this concept, continue reading.
A fireworks blast is basically a bunch of sparks quickly radiating outward from a central explosion. If you use a REALLY fast shutter speed, you'll actually freeze the sparks in mid-flight, and what you'll get are points of light in a roughly circular pattern, like this:
If you use a slightly slower shutter speed, but still fast enough to hand-hold the camera without blur, you'll get short streaks of light created by the sparks in motion. While, this is an improvement from previous example, it's still not good:
When you use a slow shutter speed (at least a few seconds), and stablize the camera (more on that later), then you capture the full trails of light that the spark leaves behind as shoot from the central explostion. This full bloom (like a flower) is the ideal.
So, the key to good fireworks photography is using a long shutter speed (at least a few seconds) to get the full bloom of the blast. Unfortunately, such a long shutter speed requires the camera to be completely stable, or else you'll get blur from the camera shaking in your hands. You don't necessarily have to use a tripod to stabilize the camera. You could use a trash can, a pole, a wall, etc.. Just make sure the camera is perfectly motionless. If you're not going to do this, then my recommendation is to just enjoy the show.
As for the other settings (ISO & aperture): Keep the ISO at the lowest settings to avoid image noise and to keep the night sky dark. Start with an aperture of f/8 or f/11 and adjust it until you get proper exposure (bright enough that there is still color color in the fireworks). In order to have control over the shutter speed, ISO, and aperture, you'll need to shoot in manual mode.