that makes the picture smooth, and not rugged in parts, this is what happens when I save my site's banner

http://www.celineonline.net/banner_dance.gif

How can I make everything smooth??

Keep in mind that gif supports at the most 256 colours, and images with lots of colours may look sharp or rugged if you save it in this format. You're probably better off saving in JPEG format for that particular image.