Could somebody please explain to me how to install games on Ubuntu 16.04? Simple instructions would be helpful.

Assuming you're talking of Linux releases, rather than Windows games under Wine (because that's an entirely different bag of worms).

1. Download the installer (a file whose name ends in .sh).
2. Make said file executable (in terminal: chmod +x filename.sh, graphically: it depends on your file manager, probably bring up a properties box for said file in some manner).
3. Run the file in whatever way you like, double-click in your file manager, type its name in the terminal, whatever.

Now you just click through the Mojoinstaller-based guide GOG now use for their Linux installers, and the game will appear on your desktop, launch menu, and in a folder called "GOG Games" in your home folder (which is the installation path they use for simplicity, rather than installing them for the whole system under /opt/ somewhere).

Please tell if you'd like more precise instructions.

If you’re using a distribution based on Debian like Ubuntu or Linux Mint, you might want to give a try to ./play.it.
This project provides scripts for a selection of games, allowing an easy installation and a better integration to the system than the "vanilla" GOG installers.

I imagine step 2 can be a bit confusing and hard to remember for a new user. Instead you could just manually run the installer through a shell, something like this:

sh Downloads/gog_dragonsphere_2.0.0.2.sh (or wherever you downloaded the file)

No need to set anything executable and you won't forget the command to run it through because it says so right there in the file extension.

Oh. Did they at least have #!/bin/bash on the first line then? Because at least the one that I mentioned had #!/bin/sh.

(Not every distro has dash as /bin/sh, but I guess the supported ones do.)

IIRC, it was #!/bin/sh, but I don't entirely remember. It's why I was considering them as installer bugs. Believe those installers have been updated since.

Thank you for showing me this! Manually running through a shell was much simpler.

Hey everyone, I', having issues with this

I get this error when attempting chmod;

chmod: cannot access 'ftl.sh': No such file or directory

the file exists, I can see it.

Any idea what I'm missing?

There's a chance you forgot to change directory to location of ftl.sh or, alternatively, you didn't provide the whole path to ftl.sh.
cd path/to/file/directory
alternatively
chmod +x path/to/file/directory/ftl.sh

Or you can use simpler way suggested by Judas. ;)

Thank you both! However, still no luck

stuart@SlaveII:/media/stuart/data/Downloads$ chmod +x gog_ftl_advanced_edition_2.0.0.2.sh

the above is entered... and nothing happens?

Commands like chmod typically produce no output if successful. Try running the program now. The command is
$ ./gog_ftl_advanced_edition_2.0.0.2.sh

(You should be able to use the Tab key to complete the filename after typing the first few characters of it. Note that the initial "./" is needed here.)

You can check the permissions of files by typing
$ ls -l
(If the output is too long, try piping it through less, like:
$ ls -l | less
)

Dziękuję Ci

This worked a treat (installed linux today)