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.
Install Firefox and Zotero on a USB drive and you can take your library with you to use on any computer.
First: download and install Portable Firefox for Windows or Mac on your USB drive. This is a special edition of Firefox designed to run entirely from a portable drive. It keeps its own settings, bookmarks and Zotero library separate from the settings installed on your computer.
Second: copy your Zotero library from your computer to your USB drive.
One way to do this is to open Zotero on your computer, click the gear button and choose Export Library (as in the image below). Save your library to a file anywhere on your computer. Then close Firefox, run Portable Firefox from your USB drive, open Zotero, click the gear button and choose Import. Import the file you just saved.
Another way to copy your library is with the Zotero sync feature. Follow the instructions on this page to set up Zotero sync on your computer. Then close Firefox, run Portable Firefox from your USB drive and set up Zotero sync there too. If you use the sync option, any changes you make to your Zotero library will update themselves in both versions of Firefox.
Just take your USB drive to the library with you, plug it into any computer and run Portable Firefox.