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) 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.
Zotero's Groups feature allows you to share references with other Zotero users online. It's a great way to work on collaborative research projects.
First, set up Zotero sync and synchronize your library.
You now have two sections in your Zotero collections pane: My Library and Group Libraries.
Personal and group libraries are entirely separate, and changes made to items in one library do not affect the other. You can drag items back and forth libraries to copy items.
Search for existing public groups or create a new group. Groups may be public (searchable, and anyone can join) or private (users can only join if invited).
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 File menu, choose Export Library, and save the file to your USB 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.