there are several videos and instructions right on Mendeley website for you to look at. you can also just google if you have very specific questions.
as @fuzzylogician said, the rule of thumb is to do your own back-up at multiple places. Mendeley does have automatic online back-up function and they give each free user 2GB of online storage, Mendeley also stores all your pdfs locally in a folder that you specify. what you can do is to save several copies of that whole folder at multiple places:
cloud storage (Dropbox, Box, OneDrive, Google Drive, etc.)
on your work computer as well as personal computer (if you have more than one)
different drives in your computer (if you have multiple)
on external hard drives (you should have at least one of this)
If you have a close friend who is interested and you can trust, you guys may look into CrashPlan. they have a free function where you and your friend install CrashPlan on your computers and connect, then it will automatically back-up your data onto your friend's computer and your friend's data onto your computer