How to backup my mac to external hard drive?

I have an iBook g4, I also have a seagate external hd. I am taking my computer in for repairs, so I want to back up my entire system. The software that the seagate came with sucks, is there a good way for me to back up my whole system? And if so, could I boot up from the external, and run my programs from there? Or should I just copy my files and applications over, by drag and dropping them? There is plenty of room on the seagate, it is a firewire connection, I am running Mac OS 10.4.11.

go get you some blank disk to do your back ups, that’s what i do as needed so good luck