Zotero's sync feature is an excellent way to create a backup for your research. It also enables you to work on your research at multiple computers. Zotero can store a copy of your library on the Zotero.org server and check it for updates whenever you open your library on a different computer. All your computers must be running the same version of Zotero.
First, set up a (free, of course) Zotero.org user account.
Repeat this configuration on each of your computers. Any updates you make on one of your computers will be reflected on the others. This even works to synchronize your library among Windows, Mac and Linux computers.
For more details and help troubleshooting sync problems, check the Zotero site.
Image credit: Kowalski, E. (2006). Lego usb flashdrive [photograph]. Retrieved from Flickr.
If you're working on a library computer, there's another easy option for taking your Zotero library with you.
Within the Zotero application, select Export Library from the File drop down menu, choose format and select whether you want the notes and/or the files exported, and save the file to your USB drive. On the new computer, open your Zotero application, select Import from the File drop down menu and find your Zotero file to import your references.
When you're done, make sure to export any changes and import the new file onto your computer. The library's computers will erase your data when you log off.