How ?

It's called a gif (ex: image.gif). Gifs are composed by a series of frames that play in a loop (making it seem like it's moving).
And gifs are not something you can do just like that. Learning how to make gifs takes a bit of time, and can be easy or dificult depending the task at hand (the ones with the eyes closing are pretty easy to make).

If you don't want to learn how to make gifs, your best shot is to steal them wherever you find em(hahaha. But it's true, most people do this).

Gifs aren't that difficult to make just take's a little time. You can do them with photo shop or even do them off some websites.

You can always do a request in the request section or go to art and graphics and request it in users sig/avatar threads.