You need to get some software to work with. Xara3d is a cool little program that does just that, make things spin.

Here are the links to a tutorial.
Part 1: http://www.talkgraphics.com/showthread.php?t=27395
Part 2: http://www.talkgraphics.com/showthread.php?t=27403

Myself, I would make a 3D model of the logo which opens up all kinds of possibilities. Xara3d is rather limited in 3D graphics production but will suffice for spinning a logo.