You press Ctrl + Print Screen to take a screen shot while playing GalCiv 2. The game might pause for a second while this is happening.

You should find the files in the "ScreenShots" folder. The location would vary depending on what OS and game version you are using. You can find all game data (the folder where all save files and ship designs are saved to) under "My Games" folder which is under "Documents". Each game version (Dread Lords, Dark Avatar, and Twlight of the Arnor) has their own separate folder.

So if you were playing TA on Windows 7, you would find the folder under:
C:\Users\<user name>\Documents\My Games\GC2TwilightArnor\ScreenShots

Odd... Have you tried taking screenshots without the folder? The game might create the folder if it finds it is missing when it needs it.

An alternative (assuming you tried to take screenshots already) is to search for files that has the characters "GC2TA". All my TA screenshots I have been taking has those characters as the first characters of the file names. Try searching under TA folder first. If that fails, then documents next. If that fails, search under the C: drive next. If that still doesn't work, you could try searching the entire computer... but I question why you haven't found it yet.

A third alternative is that you have a steam version of the game and the steam version does something differently than the version I got. Where did you get your copy any ways?