How do I back up a MAC G4 on an external hard drive?

The drive will first have to be formatted and partitioned. (Minimum one partition.) See

http://pondini.org/OSX/DU1.html

And for the G4 be sure to choose Apple Partition Map for the Partition Map Scheme.

Next, you need a backup/cloning program. You could get either Carbon Copy Cloner (paid) or SuperDuper, free for the initial backup, but you need to pay to have it run incremental backups thereafter, which of course you should do.

I use CCC.

Look at Mac Backup - Mac Backup Software, Hardware, and Guides for Your Machttp://macs.about.com/od/usingyourmac/tp/backuphub.htm and Mac OS X data backup FAQhttp://www.macmaps.com/backup.html and Important Mac Backup Tips- Time Machine, CCC, SuperDuperhttp://mikosweb.com/it-advice-blog/70-mac-backup-tips Here's a list/description of Mac backup software http://www.pure-mac.com/backup.html

The majority of Mac users use CarbonCopy Cloner @ http://www.bombich.com/software/ccc.html , or SuperDuper @ http://www.shirt-pocket.com/SuperDuper/SuperDuperDescription.html . You can also use or the Restore function of Disk Utility included in OS X.

When you backup, boot into Safe Mode (depress the Shift key at startup) and the backup will be safer and faster.

 Cheers, Tom 😉

You need at least one partition, which will make the entire (or almost the entire, since formatting itself takes some space) drive space available.

For an excellent step by step see

http://pondini.org/OSX/DU1.html