To use Proton, install Steam and then download any game through Steam. Most games will just work. Check ProtonDB, that’ll usually list what games do or don’t work, and common workarounds.
To use Wine, install Wine through whatever software store comes with your Linux distro of choice. Then download the .exe you want to run, and double click it. That should open the executable in Wine. The first time you use Wine, you may get a popup to let you install Gecko; click OK and it’ll sort itself out.
Every once in a while, a Wine update may also show a little window about updating your profile when you execute a .exe, but you don’t need to do anything with that. Just give it a few seconds.
If things break in Wine, you have four options: find an alternative that does work without going through a whole mess, launch Windows (in a virtual machine, in a dual boot configuration, whatever), deep dive into things like Wine version management and redistributables, or give up. I know enough about Wine and the Windows API that I can usually figure out what the problem is, but fixing it may not be possible without writing code so I often just give up.
I’ve only ever run into issues with video games and Microsoft Office. Neither are fixable for the mere mortal, but other games and other office programs do work, and for me that’s Good Enough.