(Please note that I'm fairly certain that these instructions to boot off of the Live CD would work similarly for Ubuntu 12.10 and the upcoming 13.04.)
To use the Ubuntu 12.04 Live CD on an iMac G3, follow my advice below.
1) First, take note of your EXACT iMac G3 model by visiting http://www.everymac.com/systems/apple/imac/index-imac.html.
2) Next, with your exact Mac model in mind, visit: http://mac.linux.be/content/xorgconf-files. Take note of the Mac models listed there and find the one that most closely matches yours. If you click one, you'll note that it opens up a page that lists at least one possible xorg.conf file that you could use for booting into the GUI; without it, you're essentially stuck with the text prompt. Also note that the xorg.conf files are just text files (ex. imac2.txt, imac5.txt, imac10.txt, and so on).
3) After you've burned the Live CD to a blank CD (or for more advanced users, if you succeeded in making a bootable USB flash drive with the Live CD image), boot off of it. For CD users, all you have to do is insert the CD, reboot (or start the computer), and hold down the 'C' key on the keyboard until your Mac starts loading stuff off of it. If you can hear your CD spinning and doing stuff, you can let go of the 'C' key.
4) When you reach an error that talks about being in "low graphics mode", you may notice that your screen may freeze for a few seconds or even up to a minute or two. After that amount of time passes, you will either be able to move your mouse around and see a cursor. If you do, proceed to step 5 below. If not, you'll have to reboot your Mac and try again.... sometimes, this can happen, but usually, after a reboot (or two), you would be able to proceed.
5) Click OK on the error, wait a bit, and you'll find yourself at a black screen with a prompt.
6) All you have to do now is use the 'wget' utility to download the appropriate xorg.conf file for YOUR Mac as described above. In my case, I have an iMac G3/600. When I go to the http://mac.linux.be site, I see that I need "imac10.txt". So, all I need to do at the prompt is type in:
wget http://mac.linux.be/files/xorg/imac10.txt
This downloads the needed file to your hard drive (don't worry about what folder it's in). If you have a different Mac model, simply use the wget utility as shown above, but make sure you use the xorg text file that pertains to YOUR Mac.
7) Next, you'll need to move the downloaded file to the /etc/X11 directory by typing in:
mv imac10.txt /etc/X11/xorg.conf
This moves the text file into the /etc/X11 directory.... and at the same time, it renames the file to xorg.conf.
8) Finally, all you need to do now is type in:
startx
If you did everything properly, you should now find yourself in the beautiful, yet sluggish, Live Ubuntu 12.04 desktop session (the environment is called "Unity"). From here, you can now double-click the icon on the desktop to install Ubuntu!
