There are two main ways to backup your Apple computer.
1. Use Time Machine to automatically backup. This is the Apple way – the easy way.
2. Manually backup your computer with some other software such as Super Duper or Carbon Copy Cloner.
If you are a beginner I recommend Time Machine. Look here.
Apple’s way (Time Machine) is a lot simpler. It’s automatic. It doesn’t rely on you remembering to do anything. The big disadvantage is that the backup is not bootable. So if your computer crashes you need to insert the original DVD and restore from the Time Machine backup. This process can take hours – not good if you are just heading out the door and need a file. But it will get your computer back to what it was like the hour before it crashed!
The second method takes a few steps longer to set up, but your backup will be bootable. That means if you plug your backup drive in, and then hold down Option-Command-Shift-Delete during startup, you can boot instantly off your backup drive. In an emergency you can plug in your backup and be running from it under a minute. You can’t do this with Time Machine. The downside it it will only take you back to THE LAST TIME YOU BACKED UP.
I do both. I have time-machine running so my most recent work is always backed up, and I do a CCC backup monthly so I have an instant bootable backup ready to go for emergencies.
This article describes how to manually backing up using Super Duper. If you want to use Time Machine as well, here’s an article on how to backup using time-machine.