Please refer to the "beginner" or "expert" sections below, depending on your familiarity with Linux.
Start downloading your favourite game from this site. When prompted by your browser, select "save". Point your browser to a known location (such as your home folder). Allow the download to complete.
The names of all our Linux games end in ".tar.gz". This is a compressed archive format and you'll need to decompress it before you can play the game.
Open your distribution's file browser and navigate to the location where you saved the file. Right-click on the file. There should be an option titled "Extract all" or similar. Select it. Depending on how automated your distribution is, the contents of the archive should be automatically placed alongside the archive itself. That is, if the archive is named "AAA.tar.gz", there should now be a directory (folder) alongside it named "AAA". It's possible that the option just says "Extract..." instead of "Extract All", which means that your package manager will load and then you'll have to find the relevant option to extract all files within your package manager's menus. You most likely will also be asked for the destination directory (that is, where the files will be extracted). The destination directory can be anywhere you like, but in all cases it's important that you extract all files and not just some of them.
If your distribution does not have a package manager, then you'll have to open a terminal window and manually extract the archive (refer to the expert section below).
Given that you now have extracted the contents of the .tar.gz in a directory on your disk, navigate to that directory (using your file browser) and execute the file named "Game_Launcher". Executing is normally achieved by double-clicking on it.
The first time you launch a game, Game_Launcher will display the End User License Agreement (EULA), which you must agree to before playing the game (this will only happen once).
Download the file to a location on your disk. Then you can either: