There are a few different avenues. Steam does have a Linux client. Here is a random guide on how to get it installed. I think that’ll work on Mint. There are a surprising amount of native Linux games available. Native games you’ll be able to download from your library right away, just as you would on Windows. For many non-native games, Steam makes it really easy to use Proton which is a compatibility tool developed by Valve. You can check protondb.com to see how well-supported a particular game is (or isn’t). Basically, to get that to work, right-click a game in your library and go to properties > compatibility > Select a proton version. Once you do this, you can download it like normal. With any luck, it’ll also launch like normal. I don’t do a ton of gaming, but this is what I’ve had the best luck with.

Aside from Steam, there are other programs such as Lutris and playonlinux, which try to make it easy to install and launch games. There are a lot of guides and info on how to use those out there. Those two are pretty popular and work well when I have used them. I’d suggest trying to do it all from Steam first, though. It should also be noted you’ll want to make sure you have appropriate graphic drivers installed or most games will run badly. Nvidia drivers can sometimes be a hassle for a lot of people to set up.