In game, there are multiple different controller configurations (and I'm hoping they add more), so the first step is to find the config closest to what you'd like so you have less to remap later and menu navigation hopefully won't be as difficult later.

I personally chose the "Simplified" & "Default" configurations, because it moved Focus to Triangle on my Dualshock, which i wanted.

Not a whole lot changes between the current options, but even saving one remap can be helpful.

With your controller plugged in/connected to your computer and recognized by Steam,
1.) In Steam, at the top left menu, you'll want to navigate to:
Steam > Settings
2.) Within the Settings menu, you'll want to navigate to the "Controller" tab on the left.
3.) Under the "External Gamepad Settings", enable the setting named, "Enable Steam Input for <insert controller type here>." For my Dualshock, that's the "generic controllers" one.
One other step you may need, depending on your controller:
Right click Gigantic in your library > Properties
In the Controller Tab, Override dropdown box; change the selection to "Enable Steam Input."

In Steam, you'll need to right-click on Gigantic in your library:
Manage > Controller Layout
Once you click "Edit Layout," you will need to navigate to each section that you want to change; the menu will save your changes along the way, and there is a reset button in case you need it.

I also published my layout if you would just like to use mine.

As stated at the start of the guide, navigating menus can be atrocious if you remap your controls like i did because none of the in game control graphics update. I just use KB+M in menus, and controller to play.

I highly recommend adding your vote to the "Suggestions to Improve Controller Experience" thread in the "Feedback and Suggestions" forum on the Official Discord requesting the devs add full controller remapping so we can use menus with controller in the future, and actually have graphics properly represented (if you're using an XBox controller).