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 of your computers must be running the same version of Zotero.
First set up a free Zotero.org user account. Then:
Repeat this configuration on each of your computers. Any updates you make on one of your computers will be reflected on the others.
For more details and help troubleshooting sync problems, check the Zotero site.
If you're working on a library computer and have a Rowan NetID, there's another easy option for taking your Zotero library with you. On your computer, click the File menu, choose Export Library, and save the file to your computer drive. On the library's computer, click the File 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.