Hello: I'm new to GoG and just purchased a game (SimCity 2000) I downloaded the Galaxy thing, I downloaded and installed my game....but....I can't find it. I expected to see an icon on my desktop. How do I find and play my game?
Thank you for your help.

There's several ways to run your game depending on how you installed it.

1> If you go to your account page on the website. https://www.gog.com/en/account
Download the offline installer and run that to install the game, it will create a short-cut on the desktop.

2> If you downloaded Galaxy and installed through Galaxy, the assumption is that you will play through Galaxy... but you don't have to.

3> If you are on Windows, you can use the start menu to play your game. You can also use it to create a short-cut on the desktop as follows:

For Windows 10
* You should see SimCity 2000 listed under recent items. Right-click on it, select More, then select Open File Location
* In the Window that pops open, highlight the SimCity 2000 icon, right-click and select copy.
* Right-click on your desktop and select paste.

This will put a copy of the SimCity 2000 short-cut on your desktop that can be used to run the game. <3

To find your game on your hard disc:
In Galaxy, go to the game page, click on that button with the two sliders on the upper right, "manage installation" -> "show directory" (or folder).

If you want to play games without Galaxy, I suggest doing what Catventurer said and download offline installers instead.
The offline installer always creates a link on the desktop.
Just remember, NOT to immediatly launch the game once installed, because that will start Galaxy again, which is kinda silly, GOG really wants us to use the client it seems.

Just to be clear about it: Both Galaxy and the offline installers install the same game files (sometimes Galaxy has a slightly more recent version). After installation, the game can be played with or without Galaxy, there is no difference. It's just the installation behaviour that's different.

In short, kick Galaxy out and run the game like it's the olden times.

My thanks to all of you who helped me. Now I can play my old SimCity!