Please note that in its support pages, Zotero.org strongly emphasizes that having a full hard-drive back-up is preferable to simply backing up or syncing a Zotero library.
1. In your desktop Zotero, go to File > Export library
2. Make sure both notes and files are clicked so you export everything!
3. Pick which format you'd like to export. We recommend exporting as a CSV for your archival copy, and also as BibLaTex, particularly if you want to import your library into other programs. BibTeX files can be used with LaTeX software to create citations and bibliographies also.
This option involves the Syncing of your Zotero collection as described under the "Synchronize your Zotero Library" section of this guide.