How can I download and store the free animated computer graphics from
http://www.cybergifs.com/ so that I could insert them into the text of
an email with the animation?

Let me know if this answers your question, and if so - I'll post in the answer box.

Right click on image, Save as, Save in MY PICTURES folder.  Remember
name of image.  (you can rename it if you wish.)

Create mail, click on body of email where you'd place your text. 
Click on INSERT, Picture, Picture Source - Click on Browse.  Browse to
MY PICTURES folder.  Find picture/image... click on body of email. 
Picture will insert.


Best regards,
tlspiegel