For Linux, you find out if there is a package. If not you go to a website and see if there is an app image or zip file. You then need to know where to place the downloaded file, how to get it running (making it executable), knowing how to chmod and chown (it is better to have to do it like in Linux, but it is an extra step), and how to add it to your desktop (there is no right+click and add to desktop/create shortcut option in Arch based distros like there is on Windows). If there is a service component you may need to go into command line and systemctl to enable it.

I don’t think I’ve ever followed that workflow to be honest. Except for when doing something niche and way above and beyond something a casual user would do.

Open the software center, search what you want. Click install. Done. I use the terminal to the same effect but that’s by preference. Installing packages as you described is not at all recommended… They won’t update with the system.

The “add to desktop” thing really depends on your Desktop Environment too. GNOME not really, KDE and most others yeah.