Plan B: export your library
If you're working on a library computer, there's another easy option for taking your Zotero library with you.
On your computer, click the Zotero gear menu, choose Export Library, and save the file to your USB drive. On the library's computer, click the gear menu, choose Import, and find your Zotero file to import it.
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.
Zotero Sync
If you're regularly using more than one computer in your research, Zotero's sync feature can keep your library up to date on all of them. 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 Zotero and be configured to sync to the server.
First, set up a (free, of course) Zotero.org user account.
Open Zotero preferences (via the gear menu) and select the Sync tab. Enter your Zotero user name and password. Check the "sync automatically" box. Zotero will upload your library to the server.
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.
Zotero File Storage
Baylor has an institutional file storage plan with Zotero, so your files will be backed up on the Zotero servers, as well as your citation data. This also means that you can use Zotero file storage for groups.
In order to take advantage of this, make sure
You have signed up for a Zotero account with your baylor.edu email address. If you did not do that originally, you can add your Baylor email address as an additional email address in your Zotero.org account settings. 
You configure your sync settings in your preferences in this manner:
