There are no specific tools required to work on GNOME design, and contributions are welcomed in any form. Pen and paper is often as good as anything else.
The following are some of the tools that are currently used by GNOME designers.
Inkscape - for mockups and icon design.
Blender - for motion mockups and some high resolution icons.
Sparkleshare - for sharing.
GTK+ Inspector - for live action.
GIMP - for editing and annotating screenshots.
There are many other free (as in beer) tools for doing design work. Here are some of them (feel free to add to the list):