What you're referring to aren't really grids; they're construction guides. The grid is just what's formed by the horizontal and vertical components.
And while some of these construction guides look really fancy and complex, they probably weren't as hard to create as you imagine. Usually, the designer starts with a general idea of what they want to build and then gradually lays down guides over a long design process. So they might end up with a very complex set of guides at the end, but they probably started with just a few horizontal and vertical lines or maybe just a single circle.
But on to the part that you probably don't want to hear...
So, remember those days way back in high school, sitting in your geometry class, listening to your math teacher drone on and on about axioms and postulates and theorems, and you muttered to yourself "when am I ever gonna use any of this stuff?" Well... this is one of those times.
That's actually why a lot of the construction guides you see are so complex—the designer needed to use geometry to find the precise positioning of one element based on another element, and they required a lot of intermediary guides to get there.
That isn't to say all of these designers aced their geometry classes. Many of them probably don't even understand the geometric theorems they're applying, and they're simply applying tricks they've picked up through trial & error aided by perhaps a little logical intuition. And this is something that most anyone can do. It just takes a little practice.