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 of Zotero.
First, set up a (free, of course) 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. 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.
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.
It is a good idea to back up your Zotero library regularly to a USB drive. While Zotero does sync with their online storage, backing up in multiple places will make a total loss of data very unlikely.
If you're using Zotero on a public computer, once you leave the machine, anyone using the computer after you will have access to your library in Zotero. This may prove an issue for some users, especially when working with confidential items.
To avoid this, there are two different options:
1. Use Zotero Web to add a few citations. Go to Zotero.org, click on the log in link in the top right of the screen and you will be able to access your library.
2. If you want to use Zotero on a public machine, be sure to save your library before ending your session. See the previous box on saving your library to a USB drive.
You may also want to uninstall Zotero after you've finished adding references to prevent future users from viewing, editing or otherwise alter your references. If you follow this route, be sure to remove your account information before ending the session so the account doesn't attempt to sync with your online account after the next user logs in. To do this, go to Zotero Preferences/Sync/Settings and then click the Unlink Account button.