There are several threads on here that show what we use as nesting boxes. This is only one of them. You can quickly see you are limited only by your imagination.
Nesting Boxes
https://www.backyardchickens.com/forum/viewtopic.php?id=41108
What chickens look for is what they perceive on their bird brains is a safe place to lay. That can be about anywhere and in anything, maybe in the middle of the coop floor or in some dark hiding place. Even shadows on the floor may convince them it is a safe place.
I know all that does not help you much but I just want to emphasize there is not one set answer for each and every chicken. No matter what I say, someone can come up with an exception. For a lot of what I'm about to say, I can come up with the exceptions.
They generally like to lay where other chickens are laying. That's where a fake egg in the nest can really help.
They generally like a darker place, a spot where they think they are hidden from predators. There are plenty of hens that lay in nests with no top and that are not all that dark, but try to keep them out of direct light.
Some seem to like tight places, some enjoy more room. There is no set answer to this.
Instead of worrying too much about what chickens like, think more about what you want. They will probably make do with about anything you provide, whether that is a bucket on the floor or some fancy wall unit.
What elevation do you want it? Think of bending over to get the eggs if you have a bad back. Think of looking in there before you stick your hand in. Ever grabbed a snake in the nest?

Talk about getting your heart pumping!!! If your coop space is tight, elevating the nest might give you a bit more floor space. The nest needs to be lower than your roosts. If the nest is at floor level, they may scratch a lot of trash in it, just messing around on the coop floor.
If the nest is elevated more than a couple of feet, it’s probably a good idea to give them a perch or intermediate step to get to the nest, but mine have no problems hopping/flying to a 5’ high roost. I think the need for this is overrated, but it is still probably a good idea.
It needs a lip on it to keep the bedding in. They'll scratch around in getting the nest in shape and may scratch the bedding, fake eggs, or real eggs already laid onto the floor.
Are you ever going to have a broody hen hatch chicks in that nest? I've seen a broody get chicks out of a ten foot high hay loft so I don't get overly excited if the nest is elevated a little, but some people on here really freak out at the thought of the nest being a little off the ground.
Some people like the nest to be moveable, either to move a broody to confinement of for ease of cleaning.
I like a top on the nests, though many people don’t have tops on theirs. A lot will depend on how it is made, but sometimes chickens will perch on the sides of the nests during the day, especially if they are confined to a coop and run. They poop a lot, even when perching during the day.
I often see two or three hens crowded into the same nest, laying at the same time. I like a bigger nest, about 16” square, to give them room. But many people do fine with smaller nests, like 12” square or maybe even smaller.
That’s about all I can think of right now. There are no set rules and no absolute requirements. Just use your imagination and maybe what is available lying around to make something unique.
Good luck!!