I believe there is a key immediately next to F12 called "print screen" If you hit that during your gameplay, it should save a screenshot in your C:\Program Files (x86)\Steam\steamapps\common\skyrim folder. Good luck!
for the f12 key you may have an 'f lock' button to toggle the functions on those keys, likely a big white F on the key if its the case (last few keyboard i've had featured one). if so give it a press and it should make f12 active for screenshots
How to Take a Screenshot
To take a screenshot, all you need to do is press the printscreen button (PrtScr) which is located in the top right area of standard North American keyboards. When you take the screenshot, you'll notice a short, one second pause in the game.
This will save your screenshot in the game directory. It should be located in the Steam\steamapps\common\skyrim\ folder, which should be in C:\Program Files\ or C:\Program Files (x86)\ unless you have installed Steam to a different directory. (Mine is just in C:\.)
If it doesn't seem to be taking any screenshots, try checking Users/(username)/My Documents/My Games/Skyrim skyrim.ini file to make sure the bAllowscreenshot function is set to 1 instead of 0.
How to Take a Screenshot Using Steam
You can also take screenshots and save them to your Steam screenshot manager by pressing the F12 button.
This only works if you have the Steam community overlay enabled. When you take the picture, Steam will inform you with a small pop-up and sound, and you will be prompted to manage your sceenshots when you exit the game. You can share your sceenshots with other people in your Steam community.
You can check out this help page if you're having problems with your Steam community overlay.