Question on animated Images

Hail to everyone!
Me and my friend are up to make a website and one of us is gonna take the graphic and multimedia part,we are at the beginning of this long road and currently learning the basics.

one of our goals is to make an animated image like http://www.blizzard.com(the hearthstone image which has beams of light or the flame effects on diablo Image) but we don't know anything about it.

from the beginning part that seems to be a drawing then painting and the final part is using adobe flash to make the image alive, i mean make the affected image like the mentioned sample, and now the question is how make these wonderful effects on images and make them affected as great as they are.[link] which part of adobe flash (or another softwares) concentrate on these wonderful effects!we don't know what its called in flash's world and books. we'd be pleased if someone shows us a path to start our project

These type of graphics are animated using Adobe After Effects.