Every game added to your steam deck's steam library (whether it is an official steam game or simply a shortcut to a game you installed some other way and are just linking to steam (right click on game or application in desktop mode and click "add to steam")) has a set of controller profiles associated with it. Your steam deck starts off with some basic templates for steam deck onboard control schemes like Gamepad Layout or WASD and Mouse Layout that map the onboard steam deck controls to what most defaults are for that type of software or game.

You can search for community layouts very easily in the steam deck's controller menu, and you can go into the settings and start changing things by simply opening up the controller layout menu and clicking edit layout. You have control over all of the buttons and inputs on the steam deck and there is a simple menu system that allows you to walk through settings for everything on your deck (buttons, joysticks, touchpads, triggers etc..).

It might seem overwhelming at first, but the good thing is that manyyyyy popular games already have controller mappings that a steam deck user in the community uploaded to steam. Just go into the community layouts tab and browse a couple steam deck layouts, try them out quick and pick the one that feels most intuitive to you and then just go. Later down the road you can get your hands dirty and tweak the little things if you want (and I promise it really isn't that overwhelming).

The starting controller layout templates can't be deleted/written over, so you don't need to worry about messing anything up either, you can always just start again from the very decent templates and defaults.

Note: If you add a non-steam game to steam so you can play it in gaming mode, make sure to rename the added game (which probably has an ugly name taken right from the name of the file .exe or whatever) to the exact name of the game. So if the non-steam game you added shows up in your library as Minecraft_v12.4_shaders or something you would want to rename it to Minecraft and then ALL of the community layouts will show up for you. An additional benefit to this is if you use the utility from Decky Loader called SteamGridDB then when you open up the settings to give your non-steam game some nice looking artwork and icons in the Steam Launcher, all of the community made steam compatible artwork for that game will show up automatically for you to select. Fast and quick, no text input needed for search, it is fantastic.

(Side note: if it is a windows program you are adding, make sure to go into the gear and set force compatibility to proton experimental, this tells the Steam Deck to run the program with proton instead of trying and failing to run it as a normal Linux program)

Press STEAM > Go to controller settings (proper, not just the layout display) > Either press on the current layout to look for a different template or press on Edit layout