Good question. You will find there is no one right answer to this. We all do something different for nest boxes and almost everything works. Open top nest boxes, closed top with or without a curtain, milk crates, litter boxes, 5 gallon buckets, huge community nest boxes, the list goes on and on.
For full sized chickens, I would not go smaller than 12" x 12". I made mine 16" x 16" in the main coop on the theory that they sometimes like to lay in the same nest at the same time and this would give them more room. Mine do lay together like that. I made mine in the tractor 12" x 12" and that worked.
As far as height, you need to put a good lip on them to keep them from scratching the nesting material and fake or real eggs out of the nest when they are getting the nesting material just the way they like it. I find a 5" lip enough, but a bit more won't hurt. Then add an 8" high hole for them to enter the nest if you are closing it in, and you have a minimum height. A little taller won't hurt but I'm not sure how necessary it is. They stand up when laying the egg so you want them to have a little head height.
Hope this helps.