1. Download and unpack the Linux version; I am using processing-1.2.1.tgz.
2. In the main directory /processing-1.2.1/ rename the java folder to something like java_old.
3. Make a symbolic link to the java version in the system, by running (in the main directory):
pfexec ln -s /usr/java .
4. MAKE SURE to disable Compiz on your desktop, otherwise it will crash your desktop and log you out, after a lot of flashing on the screen. This is in System -> Preferences -> Appearance -> Visual Effects, and select "None".
Then launch processing from the command line, with either "sh processing" or "./processing".