Night critters: Lots of animals come out at night, but most of them are difficult to photograph. You can't easily see them, you can't focus easily even if you do (more on that later), and you can only compose based on tests, not on the actual shot of a moving animal. If you add a bright light, the animals will often go away. Night wildlife is often shy.
You nearly always will need to add light. Flash is the simplest for night, and if you set your ISO high, you can get away with a smaller flash that does not have a lot of power.
The hard part can be finding the animals! If you can find a place where they feed, you can often set up before dark and wait for dark and the animals to come. Ask rangers and naturalists at parks to see if there are any places where they regularly see night wildlife. If you can get your flash away from the camera, you will have better results.
The bat photos I did recently were in front of a cave where the gray bats came to mate. They would swarm around and above the cave opening, so I had a solid idea of where they would be. The hard part was that they were constantly moving in three dimensions, movement I could not see or predict, so composition and focus were hard. At least with composition, you could do a test shot and see the overall composition even if you could not know exactly where the animals might be.
Noise: High ISOs, long exposures and underexposure all increase the appearance of noise. At night, though, you will typically be using high ISOs, long exposures, and dark areas will typically be underexposed, so if you brighten them, the noise will be revealed. So you will need to do something to reduce noise. Shooting with a newer camera or a camera with a larger sensor may help, but that might not be an option. The noise reduction sliders in Lightroom and Camera Raw are pretty good with moderate noise, but if it goes beyond that, they don't work as well.
There are many noise reduction software programs on the market and they all work. I find that Dfine from the old Nik Software plug ins still does a great job for me (and all of the old Nik Software plug-ins are free now from Google).
You may also find it helpful to apply noise reduction selectively in a photo because often the worst noise will be localized. The noise slider in Lightroom's adjustment brush can help. You can also process your image twice (or more) with noise reduction at different levels, then use layers and layer masks in Photoshop or Affinity or another program with layers to control where each amount of noise reduction is applied.
Focusing: This is something we take for granted when shooting during the day. Autofocus doesn't work too well at night! I have used my headlamp to help with autofocus on occasion and also used a flashlight for manual focus when I can.
But you can't always do that. Many times you can't use a light to help with focus (especially with wildlife), so a lot of times you have to set your focus point by guessing or estimating the distance and using that with your lens. Even little critters like spiders can be sensitive to bright light and will hide.
Then there becomes the problem of setting focus with your lens. Some lenses don't have focusing distances marked on them, and those that do can be hard to see at night unless you add a lot of light. If you shine a light on your camera, that will temporarily blind you and will alert any wildlife (or people) to your location. A red light can help, but often doesn't really do the job.
Live view can help on many cameras because there will be a focusing scale when you shoot on manual (it won't help with much else because it will likely be too dark to register anything). Live View also works for close ups – point your white light at something the same distance as your subject but away from the subject so it does not get blasted by the light. You can focus with that light, then reframe quickly (and make a quick focus adjustment if necessary).
You can't do that with moving subjects like the bats. With them, I knew the distance to background objects, then changed my focus using the focus scale to a closer distance. I would take a picture to confirm that this distance worked and readjust as necessary (this can be a bit of trial and error).
And there's a problem with that Live View scale, too. I don't know of any of these scales that give actual distances! I have ended up creating my own little scale on the back of the camera that marks key focus points from infinity to 5 feet. White or light tape with a thin magic marker works; I am having a small strip of metal engraved with these points for the back of my camera.
The key points will vary hugely depending on the focal length, which is also a problem. I am using markings for the key focal lengths I am using. I have found you really do need to do this work of creating a scale for focusing because distances on the "empty" scale that displays on Live View can be very misleading.
Moving in the dark: You have to be able to get around in the dark and also find things. You have to be able to do this at times without a lot of light. Even if you are using a light of some sort, that can be problematic because it can make your vision outside of that light (and even when it is turned off) impossible. If there is enough light (such as a full-ish moon), I will often try to work without any flashlights or head lamps.
I haven't always like head lamps and often preferred a flashlight. The reason for that is that it is easier to turn the flashlight on and off so as to use it only when needed. But with the bat work I have been doing, a headlamp is de rigueur, so I looked into other options. I found a Black Diamond Ion headlamp that I really like. It is small and lightweight, has both white and red light, but most of all, it is easy to turn on and off and adjust its brightness. It has a pressure sensitive front surface. If you swipe one way, the white light comes on, swipe again, it goes off. Swipe the other way and the red light comes on. With either light on, you can change its power by simply holding a finger against the surface. This allows you to dim down the light to make it less harsh when needed.
A red light allows you to see without affecting your night vision as much, plus it doesn't bother wildlife. Unfortunately, a red light that works best for night vision and wildlife is not very bright, so you can't always see everything you would like to see. But it helps.
So that brings me to marking gear for night work. Most photo gear is dark or black, just what you can't see at all at night! I have gotten reflective night safety adhesive strips from Home Depot and attached pieces to my tripods, camera bag, light stands and so forth. That helps a lot. It is easy to trip over a tripod or light stand leg you can't see! I have also put small pieces of this reflective night aid at strategic places on my camera.
Cameras just are not designed to be used in the dark, even with some reflective tape. So I have added some plastic raised dots on key buttons so that I can easily feel and know them in the dark. I got them from The Braille Superstore. That way I know exactly where things like my playback and display buttons are.