How do I recover from an "Update" on my MotoG?

I had my desk top all set then BOOM, the update changes things to some standard. It seems to happen with every update and that is why I keep the WiFi off. I rarely do anything with Wifi anyway.

My desktop is very simple to minimize accidental activations and to minimize confusion. The only thing I have is ONE folder and a background mage. Below that are three icons two of which are physically blocked out with cardboard taped in place and I see only the triangle pointing left.

All app icons are in a folder within that folder.

Now I have a line across the screen below the image and have two icons. My original and some (presidential vernacular) thing filled with app icons.

I recall being able to struggle through menus to get it back to my preferred set up but don't remember how I did it. Simply sliding, hold/sliding, anything from the desk top fails to do what I want.