The sole function of the Print Screen key is to copy an image of the current screen into the clipboard, after which the image can be pasted into suitable applications which support images - such as Paint, Photoshop, GIMP, or even Word.
All Logitech keyboards have this basic key. On most abbreviated keyboards, however, the Insert key doubles as the Print Screen key. This may cause a few users some confusion.
To take a screencap on most Logitech keyboards, simply hit the Print Screen key (Alt+PrtScn if you only want a screencap of the active window). This ought to be sufficient. The image is now on the clipboard, and can then be pasted into other applications.
If you suspect that the Print Screen key on your keyboard is malfunctioning, try pressing the key while holding down one or a combination of modifier keys. If you find that no image is copied onto the clipboard, try disconnecting and reconnecting the keyboard.
To double-check, try connecting your keyboard to a different computer and checking the Print Screen function.