You're kidding right? u save them like a normal pic. Except those moving pics are called gifs and they would be under the "gif" pic format and u just right click and save them.
^You play them in a window media player of some other media player and they would move. There are certain software that plays gifs and is gif compatible
u take the gif (while it's moving) and right click, select "save picture as" then save the gif where u want it. Once u uploaden it on a website, u can see it move.
When u view them in Windows Live foto Gallery, there is a couple of buttons at the buttons at the button that u can click to see the slides. I put pictures on my phone and when i look at them on that, they move.