How to actually get games running:

Download steam, make an account, log in. Go to the settings, find “Steam Play” and enable for unsupported titles. This enables Proton, which is a customized version of Wine, a Windows-Linux translation layer, plus some extra tweaks specifically for gaming. This lets you play the vast majority of all Windows games on Steam on your Linux machine.

Check out protondb to find out how compatible your chosen game is. You’ll see a rating, as well as user experiences on how well it worked, what issues they experienced, and the tweaks they made to mitigate them (take note that there is a section on each games page that is specific to the Steamdeck, Valves handheld. Not all info in this section is relevant to general PC users, so make sure you follow the more generic section).

If you look around and find a specific game that isn’t on Steam, Heroic Launcher and Lutris are your friends.

Heroic is a very nicely polished launcher for Epic Games, Amazon and GOG. It allows you to pool all three into a single library. You can use tools like winetweaks directly in the launcher, pick different Wine/proton versions per-game, etc. I’d use this as a secondary option to Steam.

Lutris also allows you to pool your games from multiple storefronts into one (Steam, Epic, EA, Ubisoft, GOG, and manually installed). Lutris can be a little complex compared to Steam and Heroic. It’s very powerful, but somewhat spartan and can also be a bit buggy in some specific instances. It’s very well suited for older games that aren’t on major storefronts, emulators, or old CD games, mainly thanks to its option to set games up via standard windows installers or add existing games by pointing lutris to their installation path.

TL;DR, Start with steam, try some cheaper/free games. A great starting point would be Valves own games, as they’re cheap and heaps of fun (Portal, Half-Life, etc). They also usually have a Linux native version so you don’t need proton (although, counterintuitively, I find Linux Native games often don’t work as well as Windows games+proton). After you get your toes wet, go for some other storefronts and library apps. Have fun and good luck, don’t be afraid to ask for help.