Are you seeking to save screen images that change (either videos or a succession of web pages that you've clicked through) or just a single image?
If it's only a single picture (whether that be of your whole screen or just part of it) Windows comes with it's own Snipping Tool built into it. You can access it from Start > All Programs > Accessories. (Hint: If you expect to use it a lot, pin it to the taskbar at the foot of your screen, so that you can access it with just a single click. To do so, go to Start > All Programs > Accessories and RIGHT-click on 'Snipping Tool', selecting 'Pin to Taskbar').
Using the snipping tool is fairly intuitive. You simply click-&drag to draw a rectangle around the part of your screen which you wish to capture. Then go to File > Save As to save the image to a location of your choice. (It's usually best to set 'JPEG' as the file type).
If you want to record your screen activity (as, for example, you click through different web pages), you'll need a special program to do it. There are hundreds of programs which can do so. See here for the best of the freebies:
http://www.techradar.com/news/the-best-free-screen-recorder