First, copy the animation file to a directory  of your website.  Let's say the name of the animation file is "anim8.swf."  Just copy that file to your website's root directory.

Second, edit the webpage(s) that will show the animation.  This part is a bit trickier, but any experienced web designer will think it is very simple.  All you have to do is decide where the animation will be, and copy/paste the following code into the page's existing HTML source:
 

<OBJECT CLASSID="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" WIDTH="400" HEIGHT="100" CODEBASE="http://active.macromedia.com/ flash5/cabs/ swflash.cab#version=5,0,0,0"> <PARAM NAME="MOVIE" VALUE="filename.swf"> <PARAM NAME="PLAY" VALUE="true"> <PARAM NAME="LOOP" VALUE="true"> <PARAM NAME="QUALITY" VALUE="auto low"> <EMBED SRC="filename.swf" WIDTH="400" HEIGHT="100" PLAY="true"  LOOP="true" QUALITY="auto low" TYPE="application/x-shockwave-flash" PLUGINSPAGE="http://www.macromedia.com/ shockwave/download/ index.cgi?P1_Prod_Version=ShockwaveFlash">  </EMBED><OBJECT>

of course, you should replace the filename.swf with the name of your own animation file.

Third, view the results with a browser that has the Shockwave plug-in.  Yes, it really is that simple!