The best way to back up is to go to File> Compressed Library (.enlx). This command will compress the .enl file and the .Data folder into one .enlx file and you'll be able to save this file to wherever you keep your backups (we recommend an external hardrive for this rather than cloud storage such as Dropbox).
If you ever need to open the compressed library, just open it as you would any other EndNote library and the EndNote program will extract the library file (.enl) and .Data folder from the compressed file for you. Only do this if you have lost your previous library, otherwise you will end up with duplicate libraries.
Synchronising is the preferred way to backup library and is highly recommended. This should be done as well as backing up your library so you effectively have two back ups if anything ever goes wrong.
How to sync your library
Go to Edit> Preferences> Sync> Click 'Enable Sync'.
Click on Sign Up and follow the steps to create an EndNote account (or link to an existing Endnote Web account)
Only one library can be used – so make it your main library. If you already have references in an EndNote Online account they will also go into your library (make sure you want this!)