First the links to get you going.

To Install --> link
Find it, and launch! --> http://getsatisfaction.com/songbird/..._how_to_launch

Cairo Dock instructions.
Assuming You have it installed in you home directory then it's time to put it into Cairo dock. (It may not even matter, since I still consider myself a Linux newbie)
Right-click on the dock. Choose "Add a custom launcher"
Command to launch on click =
Code:
Songbird/./songbird
The icon picture is in the extracted Songbird folder, so navigate to that for the pic.
Change the name if you'd like.

This worked for me so don't sling any poo