Very easy, go to the page in question, right click in a empty area and click View Source, (dont know what it is in Internet Explorer), and you'll get a window that looks something like this:

On windows it appears to come up in notepad.exe
If you read through that text you'll see the banner for animephilia, it reads
<embed src="/promo/animephilia.swf" quality=high pluginspage="http://www.macromedia.com/shockwave/download/index.cgi?P1_Prod_Version=ShockwaveFlash" type="application/x-shockwave-flash" width="760" height="50"> </embed>
so from that you can find the link of the file. in this case using this peice of information
We can see that the file is located at the following address,
http://animephilia.com/promo/animephilia.swf
so now you can open up a download manager like DownThemAll (a firefox extention) paste that into the download field and it'll download.
Please bare in mind you can find the .swf file on a webpages HTML by using "CTRL+F" or "CMD+F" on mac, and typing .swf and pressing enter/return.
Hope this helps, if you'd like me to upload a load of screenshots for you, just ask.