Have you looked at the serial examples in the Processing reference?  One stumbling block to getting it to work across different systems will be whether the Arduino is assigned to the same serial number index every time.  There are ways to deal with that problem though by looking for certain strings in the serial port name.  I'd suggest you try to get to the example I linked to above working and post back if/when you run into a specific problem.

The processing serial library works well, however it's reliability is dependent upon the reliability of the underlying device driver. I can't comment on MSWindows, but on the Mac it can be challenging. From my experience the prolific drivers, especially those fort the prolific 2303 chip are very unreliable under OSX Lion. FTDI drivers appear to be more reliable.