From what I know, windows does not save the printed screen, you have to click "print screen" And then go onto "paint" or another program and left click, or click edit, and then click paste. Print screen does not actually PRINT the screen shown, it sort of copies it so you can paste it onto another program and save it as a file.
Print screen only adds your image to the clip board, then you paste it into a program (Photoshop, Paint etc). You can get programs which save the image for you, and you can choose where you'd like it to be saved.
I use paint shop pro... its a lot cheaper than any others and better than most. Pressing print screen, going into paint/whatever and pressing ctrl+v works every time