This is for MS Outlook, so if you use another email client or Linux the procedure will differ slightly.
1) Right-click on the image. Select "Save as" (it has to be a .gif image anyway to be animated) to wherever you want to save it.
2) It has to be an HTML format email, so if you usually use plain text as I do, New Message, Format (set this to HTML), Insert > Picture > browse to the image you want to insert > OK
Have fun!
PS: Some Windows people don't accept HTML formatted email or autostrip the HTML out (for fear of malware) so it isn't guaranteed to work all the time.