I'm assuming you mean Flash/Shockwave rather than an animated gif...
To get the Flash file, you'll need to know the address pointing to the file. You'd need a decent knowledge of HTML relative addresses, but open the source of the page (cmd+opt+u in safari). Do a "find" for ".swf". Copy the address and piece together the final address (with http://www.whatever.com/root/folder). Navigate to that address in your browser to ensure you have the correct address. Copy the address and paste it into Safari's download window.
Post if you have questions, my directions are pretty vague...
Also, some complex Flash files may link to other files... at that point, it's probably not worth the trouble.
1. Download Firefox.
2. Go to the page w/ the thing you want.
3. Hit Cmd+I (or Tools / Page Info from the menu)
4. Click the "Media" tab
5. Select what you want to download.
6. Click the "Save As ..." button.