I file transfer regularly using Debian Squeeze. This won't be a million miles from Ubuntu Jaunty.
The Galazy presents as a standard USB mass storage device, so if you can do anything with a normal USB stick you should be fine. When you plug the Galaxy into the Ubuntu/Mac USB port, do you see the little USB logo at the left of the top bar on the phone? Pull down on that, to see the full notification. Under 'USB connected' it says 'Select o copy files to/from your computer'. Tap that, and you get a popup dialog with a 'Mount' button. It's only when you hit that 'Mount' button that the USB mass storage interface is activated. Once you've done that, my Squeeze box mounts the internal and external SD cards and you're away.