A "trap nest" is where you trap a hen in the nest when she goes in to lay an egg so you can see which eggs she is laying. She can't get out until you release her. If she's not going in the nest to start with a trap nest won't help. That's different to what Rosemary is talking about. I do what she's talking about. When a hen is not laying in a nest I lock her in a real nest when I see her on the wrong nest until she lays that egg. Sometimes that takes a half hour, one time it took three hours.
@Apache12 , many pullets have complete control of the egg laying process from the start. It's a really complicated process that not only includes how to put the egg together right but when and where to lay the egg. A lot of pullets don't get all that right when they start. That's why you might get a weird egg at first but usually they get things straightened out pretty fast, usually within a week or two if not a day or two.
There are different triggers that tell a hen or pullet when to release a yolk to start the internal egg making process. Daylight is an important one but there are others. The main purpose of those triggers is so she lays the egg during daytime. When pullets first start they may not get those triggers totally correct so you can get eggs laid from the roost until they work that out. Are your random eggs under the roosts?
I think this one is more likely for you. Many pullets start looking for a good nesting site abut a week before they start to lay. When that first egg comes they know where they are going. But some don't do that. For some it's as if they have no idea the egg is coming and they just drop it wherever they are. Could be in the coop or in the run. They typically gain control of that before too long.
If the eggs you are finding are scattered randomly it pretty much means they haven't gained control of the when and where yet. If a pullet doesn't put enough shell material on it you get a thin-shelled or shell-less egg that can easily be broken, either dropped from the roost or maybe one stepped on it. If something like this is going on my main suggestion is to be patient but try to pick up any randomly laid eggs.
If you are finding the eggs in the same spot every day that means the pullet has decided wherever that is makes a good nest. If that location isn't acceptable to you that's when you need to take action. You can try locking them in a real nest like Rosemary said. Something I've read about but haven't tried is to put a movable nest, maybe a box or milk crate with bedding, where they are laying. After they get used to using that nest, move it gradually a foot or so at a time, to your real nests or an acceptable spot. If you are OK with them using that nest wherever it is you are golden. If you want them in your real nests take that temporary nest away when they are in that area. Maybe they will start using your real nests.
If they are making a nest in the run or out free ranging, locking them in the coop section only for a week or so at least until they have laid that day's egg may be enough to break then of the bad habit.
Fake eggs can work. They don't always but they can. I use golf balls. Many hens and pullets like to lay where others are laying. Not all of them but a lot. A fake egg in your nests can influence them to lay there. One time I had a fake egg scratched out of the nest onto the coop floor in front of the nest. A hen laid an egg next to it on the coop floor. When I put the fake egg back in that nest (and raised the lip enough to keep them from scratching it out) she went back to laying in the nest.
This is why you need to pick up the randomly laid eggs. Another hen may see it and decide that makes a good nesting spot.
I don't know exactly what is going on with yours. But it isn't all that unique. A lot of the time they'll work it out on their own but sometimes you may have to step in Good luck!