What is an easy way to back up MacBook running 10.5.8?
Solution 1:
TimeMachine might be the easiest way to back things up on a regular basis. You'll need any old external drive and a few clicks of the mouse.
If you have more specific needs, feel free to edit your question to refine for what you are looking.
Solution 2:
Agree with bmike - TimeMachine is your best bet for an integrated system backup solution. If you're only looking to manually back up certain files, then a free solution like DropBox might work for you.