What a question. Real question is how do you want them to look? Most people favor the longer exposure and the feather look to the fireworks. Others like the clean straight tight lines. Many people like the launch trails showing and some do not. As a photographer you need to understand how to get the different looks.
First there are a couple of things you need to know for the I forgot something problem. You are better off shooting off a tripod with a cable release. Shooting on bulb and hold the shutter open for different times to get some of the effects. Shoot a couple of the practice shots they shoot and get a feel. If they do not do that, shoot a couple of the first ones and pay attention to how you set the camera.
Now the I forgot the tripod person, yes you can shoot them hand held. The finale from a festival this year, the one with all the fireworks on the black sky was shot hand held. The other ones were shot in a light rain, heavy wind on a tripod with a release. If you forgot your release, shot either hand held or on the tripod just be careful how hard you press the shutter release on the tripod. Hand held requires a little more knowledge and practice. It is not hard as you can see from the one above. I am a big fan of changing the ISO as I shoot. It also helps ID the photos later. The finale of most fireworks puts a lot of light in the center so you need to reduce the exposure time, increase the f-stops and decrease the ISO. I still keep the shutter speed up if I am hand holding the camera so I can semi freeze the fireworks.
If you shoot and hold the shutter open about 1-3 seconds with a moderate ISO and shutter speed you can get pretty good shots. I use somewhere between 5.6 and 11 as the f-stop.
One thing people forget is the distance you are from the fireworks. The farther away you are the more dark the shots will be and the more dark sky you will have. The shots can be cropped and look pretty good if you shoot the images correctly. I am not going to give you advice on what to set the camera on as you can get that everywhere but you need to decide how you want the shots to look before you even think about how to set the camera.
Two secrets, one, set the camera and the lens on manual. The lens will keep trying to focus the whole time the firework is moving and changing on automatic. You may not get the shots you want. Set the lens to infinity to keep things simple. The other trick is the ISO. Most can be set on automatic. I use manual almost 100 percent of the time. The photos in the slideshow has the ISO listed. The finale is shot at 3200 which is against everything you will see on the net. It works because of the amount of darkness around the display. It also allows it to be hand held and shot without a problem.
My first few times I kept records as they were shot on slides. You have an advantage because of the display. Look at the shots and make adjustments. It should only take a shot or two if you know something about your camera.
The compact camera crowd or point and shot are not left out. The first thing you need to do is shut of the flash. Nothing more irritating than someone shooting in the dark at fireworks and screwing up all the others shots because they do not know the flash is good for about 10 feet.
You can get the information from the manuals but most have the settings on the camera that will work.
You need to set the camera to M and the func can be set if you wish I would use it on 0. I would then press menu and set the time you want it to keep open. It may just say how many seconds. That should be set about 1-4 to begin with.
Since all pocket cameras are not the same I will leave it at that. If you have questions you can call the manufacturer for help if you cannot locate the manual. You also can download the manual from the manufacturer’s site.
Some cameras like the S8100 Nikon ( I am familiar with that one) has stabilization built in. You can set it to night photography and see how it does. If you set it to night portrait the flash will fire. That is disturbing to the others. It has 17 various modes to shoot in when you change things. You can also just set it on auto and give it a try.