If you want to get a document printed that uses screen shots, you can use separate software to capture images on your monitor, but in the end a screen shot will only be made of what’s on the screen, so the built-in facility of the operating system is normally enough.
The three factors that make (or ruin) screen shot reproduction are resolution, colour conversion and file format (compression).
The resolution of the screen on which you take the shot is important: the higher the better. If you capture a 1680 x 1050 screen you will get a 5 MB RGB (6.8MB in CMYK) file which even at 300 dpi is definitely good enough for a reproduction at a size of 14 x 9 cm. Even larger sizes (up to A4) are usually fine.
The colour of the screen shot is obviously RGB, so as with any image you need to take care when converting to not lose the vibrancy. The colour profile for high quality sheetfed offset will get much better results than the Photoshop default of North American Standard Web Offset.
Finally you need to be careful not to use any lossy compression, which would cause artefacts and blur the image. JPEG compression is such a compression method, you lose quality every time you save. For screen shots tiff files with lzw compression usually work best.
So capture an image at the highest possible resolution, maintain the colour vibrancy and don’t use lossy compression when saving the image, or the complete (pdf-) document.