Here's how the Print screen button key on a keyboard should work.
The Print Screen (or PrtScrn or variant thereof) key does not immediately print the screen as the name might suggest – it’s a bit misleading. Instead it copies the current screen image to your clipboard. You can then paste this image into a suitable photo-editing (or similar) type program so that you can edit it or print it out from there.
This what you're specifically after:
An alternative way to the above is pressing Alt + Print Screen on your keyboard - this does exactly the same as the above, but the image copied to the clipboard is only that of the currently active window.
An alternative to using the Print screen key to capture screen images is the Snipping Tool. Please see: