What is an easy way to back up MacBook running 10.5.8? What's an easy way to back up the files on a Macbook that is running OS 10.5.8  ?

As far as I can see, I think iCloud only works with 10.7.2 and above, and MobileMe is not accepting new accounts...
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.