I shot these at ISO 100, F16 or 18, and a shutter speed of about 10-15 seconds.
Here’s the explanation I wrote for my local camera group.
First, the ISO. We are used to thinking that night images require a high ISO. That's TRUE if you are hand-holding your camera or shooting a moving object like people, but in this case we must be using a good tripod, so that takes care of camera shake. We aren't trying to freeze the rides since the carnival midday is just the foundation of the image and their movement just screams the activity of large groups of funnel-cake-eating people. Bottom line is, use a low ISO, maybe 100 or 200 for maximum color fidelity.
Focus is next. Point your AF camera at an empty sky and it won't know what to do. It'll likely keep shifting focus in a vain attempt to find an object on which to focus. Ain't gonna happen so switch to MANUAL focus and focus on the farthest object you can find at the carnival. Then LEAVE that focus at that distance, which will be far enough way to simulate infinity.. Check it from time to time to make sure you don't bump it.
Aperture. Yeah, it's dark outside, but the rides and fireworks are extremely bright, so a wide aperture is not your friend. That would require a relatively fast exposure of 2-3 seconds or so for the rides and the fireworks would be waaaay overexposed. Reduce your aperture to f11 or f16, maybe even smaller. That will keep the fireworks from overexposing. Fireworks look their best when they have time to burst and spread out across the sky while the shutter is open longer, so a small aperture will force you to use a longer shutter speed. And that's what you want.
Lastly, shutter speed. We set the ISO (100 or 200) and the aperture (F11, 16 or 9). Now start with a 10 or 12 second exposure. GENTLY press the shutter right after you hear the rockets launch and before they burst. If you are lucky there will be 2 or 3 bursts during the time your shutter is open. The fireworks do the work of simply painting themselves across the image.
Lens? An 18-55 kit lens will do fine. Use the slightly WA range if you are close enough. On full frame 35mm is ideal.
And be sure to leave plenty of empty sky in your viewfinder so the shells have room to do their work. Remember, some burst really high and wide and can dominate the image in a spectacular way You don't want to miss them. Now, get out there and get to work. Don't forget a lawn chair