First, you need to tell Mathematica where to save the files,
by executing something like this:
Then make your plot, and assign it a name:
The following Mathematica command will then save your plot as a GIF file:
which looks like this in a web page:
It's just as easy to get a JPG:
which looks like this:
You can directly adapt the same Input cell to get encapsulated postscript (which has resolution limited only by the display device):
Many other graphics formats are available in the same way.
The animation can be exported as an animated GIF, thus:
The animated GIF, sinemovie.gif, is displayed at the top of this web page, but it runs only once, and it's easy to miss!
If you want the animation to run repeatedly, include a "ConversionOption" like this:
Here's the resulting animated GIF:
First a JPG:
which apparently has some anti-aliasing and color distortion that the GIF (below) doesn't have.