Title says it all. Do we have any evidence for how the Marauders map actually shows the different floors of Hogwarts, and whether the user has any control of this? Answers should ideally be from the books!
In the books
Except for the moving dots and names, it would probably work like any other regular map we have. There are no mentions of any flaps or folds on the map, which makes the whole thing even more confusing.
I like to think that's it's one big, flat map that shows all the floors at a glance. JKR specifically mentioned how small the dots and names were - which I imply as the map being so cramped (having all the floors on the surface) that the dots and names seem so tiny.
It was a map showing every detail of the Hogwarts castle and grounds. But the truly remarkable thing were the tiny ink dots moving around it, each labeled with a name in minuscule writing. Astounded, Harry bent over it. A labeled dot in the top left corner showed that Professor Dumbledore was pacing his study; the care- taker’s cat, Mrs. Norris, was prowling the second floor; and Peeves the Poltergeist was currently bouncing around the trophy room. And as Harry’s eyes traveled up and down the familiar corridors, he noticed something else.
It's also worth mentioning that Harry could roll up the map. Assuming it was folded, I'd expect that it would have been quite hard to roll a likely 7 paper-thick map and keep it rolled in your pocket. Of course, this is The Wizarding World we're talking about, and anything's possible.
Then, quite suddenly, as though following orders, he rolled up the map, stuffed it inside his robes, and hurried to the door of the classroom.
In the movies
Here's what Miraphora Mina, designer of the Marauder's Map, has to say about the movie's version of it:
"The thing is, it's designed in such a way where when you unfold it, it's a mystery," Lina said. "You don't quite know what layer you're on. It's like a scroll. And so we were able to keep adding new layers of map, and layers of school, into the design of it."
As the films progressed, she added new things to different layers of the map. The map was based on the architectural drawings of Hogwarts made by Stuart Craig. Because it's it's enormous, it's folded up to become portable.
In the films it's handled very simply. The floors are stacked one on top of the other in folded layers. Simply turn over the fold and you can see the floor above and below.