This is basically a strategy question: what, where and when all together. "How" is not really relevant: there are tons of back-up programs out there and they all do the same basic thing: make copies of data.
But the real question is: are these back-up programs making copies of the data important to you? How should you install&run Ubuntu while safeguarding your data?
There is no "one size fits all" when it comes to computers, Ubuntu versions or a backup strategy, therefore I've split this up into 5 basic user types with each their own answer:
- I don't have a computer!
- My computer doesn't contain my life…
- My computer contains my life!
- My computer IS my life! (or you're running in UEFI mode!)
And as the above does not fit everyone, one for the impatient:
So click one of the above links and go to your user type!
P.S. If you're running a server farm and you've read this question so far, I'm sorry: this is about a single PC, not a network, nor a server farm.