If you go into a game's properties in Steam (the little gear icon), and and then choose "Compatibility" from the resulting window, you can choose a version of Proton to run the game, usually the latest stable is good, sometimes you have to play around to find a good version.
Once you've chosen a Proton version, the option to "Install" will be available in your game menu.
I gave up on Windows a couple years ago, and most Steam games run in Linux using Proton through Steam. Some modern titles with fancy DRM don't work, but I generally don't buy those anyway (Denuvo, certain anticheats, etc).
For non-Steam games, I do the same thing, either with Steam (by adding a non-steam game installer, and using proton to install it), or by using Lutris (https://lutris.net/). I generally use Lutris with my GoG library.
Once you've chosen a Proton version, the option to "Install" will be available in your game menu.
I gave up on Windows a couple years ago, and most Steam games run in Linux using Proton through Steam. Some modern titles with fancy DRM don't work, but I generally don't buy those anyway (Denuvo, certain anticheats, etc).